함수와 그래프 전체 문제

Subtract Rational Expressions with a Common Denominator

In the following exercises, subtract.

$\frac{5{q}^{2}+3q-9}{{q}^{2}+6q+8}-\frac{4{q}^{2}+9q+7}{{q}^{2}+6q+8}$

Subtract Rational Expressions with a Common Denominator

In the following exercises, subtract.

$\frac{5{r}^{2}+7r-33}{{r}^{2}-49}-\frac{4{r}^{2}+5r+30}{{r}^{2}-49}$

Subtract Rational Expressions with a Common Denominator

In the following exercises, subtract.

$\frac{7{t}^{2}-t-4}{{t}^{2}-25}-\frac{6{t}^{2}+12t-44}{{t}^{2}-25}$

Add and Subtract Rational Expressions whose Denominators are Opposites

In the following exercises, add.

$\frac{10v}{2v-1}+\frac{2v+4}{1-2v}$

Add and Subtract Rational Expressions whose Denominators are Opposites

In the following exercises, add.

$\frac{20w}{5w-2}+\frac{5w+6}{2-5w}$

Add and Subtract Rational Expressions whose Denominators are Opposites

In the following exercises, add.

$\frac{10{x}^{2}+16x-7}{8x-3}+\frac{2{x}^{2}+3x-1}{3-8x}$

Add and Subtract Rational Expressions whose Denominators are Opposites

In the following exercises, add.

$\frac{6{y}^{2}+2y-11}{3y-7}+\frac{3{y}^{2}-3y+17}{7-3y}$

In the following exercises, subtract.

$\frac{{z}^{2}+6z}{{z}^{2}-25}-\frac{3z+20}{25-{z}^{2}}$

In the following exercises, subtract.

$\frac{{a}^{2}+3a}{{a}^{2}-9}-\frac{3a-27}{9-{a}^{2}}$

In the following exercises, subtract.

$\frac{2{b}^{2}+30b-13}{{b}^{2}-49}-\frac{2{b}^{2}-5b-8}{49-{b}^{2}}$

In the following exercises, subtract.

$\frac{{c}^{2}+5c-10}{{c}^{2}-16}-\frac{{c}^{2}-8c-10}{16-{c}^{2}}$

Sarah ran 8 miles and then biked 24 miles. Her biking speed is 4 mph faster than her running speed. If $r$ represents Sarah’s speed when she ran, then her running time is modeled by the expression $\frac{8}{r}$ and her biking time is modeled by the expression $\frac{24}{r+4}.$ Add the rational expressions $\frac{8}{r}+\frac{24}{r+4}$ to get an expression for the total amount of time Sarah ran and biked.

If Pete can paint a wall in $p$ hours, then in one hour he can paint $\frac{1}{p}$ of the wall. It would take Penelope 3 hours longer than Pete to paint the wall, so in one hour she can paint $\frac{1}{p+3}$ of the wall. Add the rational expressions $\frac{1}{p}+\frac{1}{p+3}$ to get an expression for the part of the wall Pete and Penelope would paint in one hour if they worked together.

Donald thinks that $\frac{3}{x}+\frac{4}{x}$ is $\frac{7}{2x}.$ Is Donald correct? Explain.

Explain how you find the Least Common Denominator of ${x}^{2}+5x+4$ and ${x}^{2}-16.$

Add: $\frac{7}{10}+\frac{8}{15}.$

Subtract: $6(2x+1)-4(x-5).$

Find the Greatest Common Factor of $9{x}^{2}{y}^{3}$ and $12x{y}^{5}$.

Factor completely $-48n-12$.

Find the LCD for $\frac{8}{{x}^{2}-2x-3},\frac{3x}{{x}^{2}+4x+3}$.