Rewrite the rational expressions in simplest form:
1) \(\Large{\frac{15x^3}{20x^2-5x}}\)
2) \(\Large{\frac{4x^3-36x}{4x^3-10x^2-6x}}\)
3) Which of the following expressions is already in simplest form?
a) \(\Large{\frac{x^2+6x+8}{x^2-4}}\)
b) \(\Large{\frac{x^2+7x+12}{x^2-4x+3}}\)
c) \(\Large{\frac{x^2+3x-10}{x^2+x-6}}\)
d) \(\Large{\frac{x^2-1}{x^2+7x+6}}\)
4) Which of the following expressions is already in simplest form?
a) \(\Large{\frac{x^3-8}{x^2-4}}\)
b) \(\Large{\frac{3x^2-13x-10}{x^2-3x-10}}\)
c) \(\Large{\frac{2x^2+x-6}{x-6}}\)
d) \(\Large{\frac{4x^2-25}{2x^2-5x-25}}\)
Rewrite the rational expressions in simplest form:
5) \(\Large{\frac{x^3-9x^2+18x}{2x^2-18}\cdot\frac{8x^3+24x^2}{x^2-4x-12}}\)
6) \(\Large{\frac{x^2+9x-10}{-5x+5}\div\frac{x^2-1}{1-x}}\)
7) \(\Large{\frac{x^3-5x^2-14x}{3x^3-21x^2}}\normalsize\div(2x^2+14x+20)\)
8) \(\Large{\frac{x^3+27}{2x^2+7x+3}\cdot\frac{4x^2-1}{10x^2-5x}}\)
9) \(\Large{\frac{x^3+x^2-9x-9}{x^3+1}\cdot\frac{7x^3-7x^2+7x}{x^2-6x+9}}\)
10) \(\Large{\frac{25x^2-10x+1}{x^2+2x-15}\div\frac{5x^2-16x+3}{2x^2+20x+50}}\)
Write the missing rational expression that completes the given equation.
11) \(\Large{\frac{x^2+3x-28}{x^2+4x}\cdot\:\:\large?=\Large\frac{(x-4)^2}{x(x-1)}}\)
12) \(\Large{\frac{4x^3-100x}{x^2-2x-15}\div\:\:\large?=\Large\frac{2(x-3)}{x}}\)
Identify the Least Common of the following rational expressions:
13) \(\Large{\frac{x+4}{x-3}}\) and \(\Large{\frac{x-5}{x+2}}\)
14) \(\Large{\frac{x^2-3x+2}{2x^2-10x}}\) and \(\Large{\frac{x^2-4}{5x^2}}\)
15) \(\Large{\frac{4x}{x^4+8x^3+16x^2}}\) and \(\Large{\frac{2x-1}{x^3-16x}}\)
Add or subtract the rational expressions:
16) \(\Large{\frac{x^2-3x}{x-8}+\frac{5x-3}{x-8}}\)
17) \(\Large{\frac{5x^2-10}{x-4} -\frac{3x^2+4x+6}{x-4}}\)
18) \(\Large{\frac{x+3}{x-3}+\frac{x-3}{x+3}}\)
19) \(\Large{\frac{x+4}{8x-4}-\frac{2}{2x^2-7x+3}}\)
20) \(\Large{\frac{2}{x^2-36}+\frac{x+8}{x^2-12x+36}}\)
Solution Bank
1) \(\Large{\frac{15x^3}{20x^2-5x}}\)
2) \(\Large{\frac{4x^3-36x}{4x^3-10x^2-6x}}\)
3) Which of the following expressions is already in simplest form?
a) \(\Large{\frac{x^2+6x+8}{x^2-4}}\)
b) \(\Large{\frac{x^2+7x+12}{x^2-4x+3}}\)
c) \(\Large{\frac{x^2+3x-10}{x^2+x-6}}\)
d) \(\Large{\frac{x^2-1}{x^2+7x+6}}\)
4) Which of the following expressions is already in simplest form?
a) \(\Large{\frac{x^3-8}{x^2-4}}\)
b) \(\Large{\frac{3x^2-13x-10}{x^2-3x-10}}\)
c) \(\Large{\frac{2x^2+x-6}{x-6}}\)
d) \(\Large{\frac{4x^2-25}{2x^2-5x-25}}\)
Rewrite the rational expressions in simplest form:
5) \(\Large{\frac{x^3-9x^2+18x}{2x^2-18}\cdot\frac{8x^3+24x^2}{x^2-4x-12}}\)
6) \(\Large{\frac{x^2+9x-10}{-5x+5}\div\frac{x^2-1}{1-x}}\)
7) \(\Large{\frac{x^3-5x^2-14x}{3x^3-21x^2}}\normalsize\div(2x^2+14x+20)\)
8) \(\Large{\frac{x^3+27}{2x^2+7x+3}\cdot\frac{4x^2-1}{10x^2-5x}}\)
9) \(\Large{\frac{x^3+x^2-9x-9}{x^3+1}\cdot\frac{7x^3-7x^2+7x}{x^2-6x+9}}\)
10) \(\Large{\frac{25x^2-10x+1}{x^2+2x-15}\div\frac{5x^2-16x+3}{2x^2+20x+50}}\)
Write the missing rational expression that completes the given equation.
11) \(\Large{\frac{x^2+3x-28}{x^2+4x}\cdot\:\:\large?=\Large\frac{(x-4)^2}{x(x-1)}}\)
12) \(\Large{\frac{4x^3-100x}{x^2-2x-15}\div\:\:\large?=\Large\frac{2(x-3)}{x}}\)
Identify the Least Common of the following rational expressions:
13) \(\Large{\frac{x+4}{x-3}}\) and \(\Large{\frac{x-5}{x+2}}\)
14) \(\Large{\frac{x^2-3x+2}{2x^2-10x}}\) and \(\Large{\frac{x^2-4}{5x^2}}\)
15) \(\Large{\frac{4x}{x^4+8x^3+16x^2}}\) and \(\Large{\frac{2x-1}{x^3-16x}}\)
Add or subtract the rational expressions:
16) \(\Large{\frac{x^2-3x}{x-8}+\frac{5x-3}{x-8}}\)
17) \(\Large{\frac{5x^2-10}{x-4} -\frac{3x^2+4x+6}{x-4}}\)
18) \(\Large{\frac{x+3}{x-3}+\frac{x-3}{x+3}}\)
19) \(\Large{\frac{x+4}{8x-4}-\frac{2}{2x^2-7x+3}}\)
20) \(\Large{\frac{2}{x^2-36}+\frac{x+8}{x^2-12x+36}}\)
Solution Bank