2024.01.15_Simplify_Rational_Expressions

Question 1

$$\textrm{Simplify:}\frac{2x^3-6x^2-108x}{x^3+x^2-30x}$$

Accepted Answer

$$\frac{2(x-9)}{x-5}$$

Answer

$$\frac{2x(x+6)}{x-5}$$

Answer

$$-\frac{(x-9)}{(x+6)}$$

Question 2

$$\textrm{Simplify: }\frac{-x^2-12x-32}{2x^2+16x+32}$$

Accepted Answer

$$-\frac{x+8}{2(x+4)}$$

Answer

$$\frac{x-8}{x-4}$$

Answer

$$\frac{2}{x+4}$$

Question 3

$$\textrm{Simplify: }\frac{(x+5)(x^2+3x-18)}{(x-3)(2x^2+11x+5)}$$

Accepted Answer

$$\frac{x+6}{2x+1}$$

Answer

$$\frac{x+5}{x-3}$$

Answer

$$\frac{(x-5)(x-6)}{3}$$

Question 4

$$\textrm{Simplify: }\frac{2x^2+6x-8}{-3x^2-9x+12}$$

Accepted Answer

$$-\frac{2}{3}$$

Answer

$$\frac{-3(x-4)}{x+1}$$

Answer

$$\frac{2(x+4)}{3}$$

Question 5

$$\textrm{Simplify: }\frac{5x^2-13x-6}{5x^2-5x-30}$$

Accepted Answer

$$\frac{5x+2}{5(x+2)}$$

Answer

$$\frac{5}{x-2}$$

Answer

$$-\frac{5(x+2)}{x-3}$$

Question 6

$$\textrm{Simplify: }\frac{-x^2-18x-81}{x^2-81}$$

Accepted Answer

$$-\frac{x+9}{x-9}$$

Answer

$$-1$$

Answer

$$\frac{x-9}{9}$$

Question 7

$$\textrm{Simplify: }\frac{2x^3-32x}{8x-2x^2}$$

Accepted Answer

$$-(x+4)$$

Answer

$$\frac{x^2+4}{2x}$$

Answer

$$-\frac{x+4}{x-4}$$

Question 8

$$\textrm{Simplify: }\frac{(x-3)(x^2-9x+8)}{(3x-3)(x^2-14x+33)}$$

Accepted Answer

$$\frac{x-8}{3(x-11)}$$

Answer

$$\frac{3(x-8)}{2(x-1)}$$

Answer

$$\frac{-3}{x+11}$$

Question 9

$$\textrm{Simplify: }\frac{x^3-7x^2+5x-35}{x^2-14x+49}$$

Accepted Answer

$$\frac{x^2+5}{x-7}$$

Answer

$$x+5$$

Answer

$$\frac{x-7}{x-5}$$

Question 10

$$\textrm{Simplify: }\frac{4x^3-24x^2}{6x^2-42x+36}$$

Accepted Answer

$$\frac{2x^2}{3(x-1)}$$

Answer

$$\frac{4x^2}{3}$$

Answer

$$\frac{x-6}{x-1}$$

Question 11

$$\textrm{Simplify: }\frac{-10x^2+60x+160}{-5x^2+20}$$

Accepted Answer

$$\frac{2(x-8)}{x-2}$$

Answer

$$-\frac{10(x+2)}{5}$$

Answer

$$\frac{5x-3}{x-8}$$

Question 12

$$\textrm{Simplify: }\frac{3x^2-7x-6}{x^2-9}$$

Accepted Answer

$$\frac{3x+2}{x+3}$$

Answer

$$\frac{x-3}{x+3}$$

Answer

$$\frac{3x}{2x+1}$$

Question 13

$$\textrm{Simplify: }\frac{2x^2+5x+2}{-x^2-4x-4}$$

Accepted Answer

$$-\frac{2x+1}{x+2}$$

Answer

$$\frac{x+2}{x+1}$$

Answer

$$-2x+1$$

Question 14

$$\textrm{Simplify: }\frac{2x^2-5x+3}{6x-4x^2}$$

Accepted Answer

$$-\frac{x-1}{2x}$$

Answer

$$\frac{2(x-1)}{x}$$

Answer

$$\frac{2x+1}{2x-1}$$

Question 15

$$\textrm{Simplify: }\frac{2x^2-5x+3}{6x-4x^2}$$

Accepted Answer

$$-\frac{x-1}{2x}$$

Answer

$$\frac{2(x-1)}{x}$$

Answer

$$\frac{2x+1}{2x-1}$$

Question 16

$$\textrm{Simplify: }\frac{4x^2-1}{6x+3}$$

Accepted Answer

$$\frac{2x-1}{3}$$

Answer

$$\frac{2x+3}{2x-3}$$

Answer

$$\frac{2}{x+3}$$

Question 17

$$\textrm{Simplify: }\frac{5x-45}{x^2-17x+72}$$

Accepted Answer

$$\frac{5}{x-8}$$

Answer

$$-\frac{9}{x-8}$$

Answer

$$\frac{x+9}{x+8}$$

Question 18

$$\textrm{Simplify: }\frac{4x^2+5x-6}{4x^2-16x-48}$$

Accepted Answer

$$\frac{4x-3}{4(x-6)}$$

Answer

$$\frac{x+2}{x-6}$$

Answer

$$\frac{4x+3}{4}$$

Question 19

$$\textrm{Simplify: }\frac{3x^2+18x+15}{3x^2-2x-5}$$

Accepted Answer

$$\frac{3(x+5)}{3x-5}$$

Answer

$$\frac{3x-5}{x+1}$$

Answer

$$\frac{x+1}{3}$$

Question 20

$$\textrm{Simplify: }\frac{2x^2-4x-48}{4x^2+24x+32}$$

Accepted Answer

$$\frac{x-6}{2(x+2)}$$

Answer

$$\frac{2(x-6)}{x+4}$$

Answer

$$-\frac{x+4}{2}$$

Question 21

$$\textrm{Simplify: }\frac{x^2-x-12}{x^2-8x-48}$$

Accepted Answer

$$\frac{x+3}{x+12}$$

Answer

$$\frac{x-3}{x-4}$$

Answer

$$\frac{x+12}{x-16}$$

Question 22

$$\textrm{Simplify: }\frac{x^2-10x+25}{x^2-25}$$

Accepted Answer

$$\frac{x-5}{x+5}$$

Answer

$$\frac{x-10}{x+10}$$

Answer

$$-\frac{5(x+1)}{x-1}$$

Question 23

$$\textrm{Simplify: }\frac{x^2-12x+11}{x^2-x-110}$$

Accepted Answer

$$\frac{x-1}{x+10}$$

Answer

$$\frac{x-11}{x+11}$$

Answer

$$-\frac{1}{10}$$

Question 24

$$\textrm{Simplify: }\frac{2x^2-2x-40}{x^2-x-20}$$

Accepted Answer

$$2$$

Answer

$$\frac{x+4}{x+5}$$

Answer

$$-\frac{1}{2}$$

Question 25

$$\textrm{Simplify: }\frac{x^2-7x-18}{x^2-19x+90}$$

Accepted Answer

$$\frac{x+2}{x-10}$$

Answer

$$\frac{x-18}{x+9}$$

Answer

$$\frac{x-6}{x+6}$$

2024.01.15_Simplify_Rational_Expressions

Create a free account to finish this quiz

Information

Feedback

What do you think of the new look?