Simplify the expression
${\displaystyle \frac{2y^4}{xy-4y}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{x^2-8x\mathrm{+12}}{x^2-3x\mathrm{+2}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{2x-2}{x-1}+\frac{2-x}{x-1}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle 3-\frac{5}{x-4}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{1}{x\mathrm{+4}}-\frac{1}{x\mathrm{+7}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

If you rationalize the denominator of
${\displaystyle \frac{1}{5x\sqrt{5}-3y\sqrt{3}}}$
then you will get
${\displaystyle \frac{A}{B}}$



where A = __________________

and B = __________________

If you rationalize the numerator of
${\displaystyle \frac{\sqrt[3]{x^2}\mathrm{+1}\sqrt[3]{x}+1}{\sqrt{x^3}-1}}$
then you will get
${\displaystyle \frac{A}{B}}$



where A = __________________

and B = __________________

Simplify the expression
${\displaystyle \frac{x^2\mathrm{+5}x\mathrm{+6}}{x^2\mathrm{+3}x\mathrm{+2}}c\stackrel{.}{\frac{x^2\mathrm{+6}x\mathrm{+5}}{x^2\mathrm{+4}x\mathrm{+4}}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{2x^2\mathrm{+7}x\mathrm{+3}}{x^2\mathrm{+2}x-8}÷\frac{x^2\mathrm{+4}x\mathrm{+3}}{2x^2-5x\mathrm{+2}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{1}{x\mathrm{+4}}-\frac{1}{x\mathrm{+7}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{4x}{{\left(x\mathrm{+2}\right)}^2}+\frac{1}{x\mathrm{+2}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle x\mathrm{+2}+\frac{3}{x\mathrm{+2}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{2}{x^2}+\frac{1}{x^2+x}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{x^2-4x\mathrm{+4}}{x^2-5x\mathrm{+6}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{1}{x^2\mathrm{+3}x\mathrm{+2}}-\frac{1}{x^2-3x-4}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{1+\frac{4}{c-4}}{1-\frac{4}{c-4}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(c\right)}{g\left(c\right)}.}$

Your answer for the function ${\displaystyle f\left(c\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(c\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{\frac{6}{x-1}-\frac{1}{x\mathrm{+1}}}{\frac{x}{x-1}+\frac{1}{x\mathrm{+1}}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

Simplify the expression
${\displaystyle \frac{\frac{2}{a+h}-\frac{2}{a}}{h}}$
and give your answer in the form of
${\displaystyle \frac{A}{B}.}$

Your answer for ${\displaystyle A}$ is : __________________
Your answer for ${\displaystyle B}$ is : __________________

Simplify the expression
${\displaystyle \frac{y^2\mathrm{+4}y}{y^2-16}}$
and give your answer in the form of
${\displaystyle \frac{f\left(y\right)}{g\left(y\right)}.}$

Your answer for the function ${\displaystyle f\left(y\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(y\right)}$ is : __________________

Rationalize the denominator of expression
${\displaystyle \frac{2}{4+\sqrt{7}}}$

= __________________ / __________________

Simplify the expression
${\displaystyle \frac{7x^3-11x^2-6x}{6x^2-14x\mathrm{+4}}}$
and give your answer in the form of
${\displaystyle \frac{f\left(x\right)}{g\left(x\right)}.}$

Your answer for the function ${\displaystyle f\left(x\right)}$ is : __________________
Your answer for the function ${\displaystyle g\left(x\right)}$ is : __________________

The expression
${\displaystyle \sqrt[5]{v^{35}}}$
equals __________________

Write the following as a simple fraction in lowest terms.


${\displaystyle \frac{{\left(-3\right)}^{-4}+{\left(-3\right)}^{-2}}{{-3}^{-3}}}$
__________________

The total resistance, R, of a particular group is given by the formula:
${\displaystyle R=S+\left(\frac{1}{\frac{1}{T}+\frac{1}{U}}\right)}$


This formula can be simplified to the form ${\displaystyle \frac{A}{B}}$ where A and B contain no fractions.
A = __________________
B = __________________


Suppose that ${\displaystyle S=11\Omega ,T=90\Omega \text{and}U=84\Omega }$.
Then R = __________________ Note: Your answer must be a decimal.