A1: Simplifying Rational Expressions (already factored)

Simplify the following

• 
• 
• 
• 

Tags

CCSS.HSA.APR.D.6

Simplify by cancelling

• 1

• -1

• Can't be simplified

Answer explanation

To simplify, we can cancel common factors in the expression. The result after cancellation leads to -1, making it the correct answer.

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(x+2)(x-3)}{(x+2)(x+5)} \), we can cancel the common factor \( (x+2) \) from the numerator and denominator, resulting in \( \frac{x-3}{x+5} \). Thus, the correct answer is \( \frac{x-3}{x+5} \).

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(2x-4)(x+1)}{(2x-4)(x-1)} \), we can cancel the common factor \( (2x-4) \) (as long as \( x \neq 2 \)). This gives us \( \frac{x+1}{x-1} \), which is the correct answer.

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(3x+6)(x-2)}{(3x+6)(x+4)} \), we can cancel the common factor \( 3x+6 \) from the numerator and denominator, resulting in \( \frac{x-2}{x+4} \). Thus, the correct answer is \( \frac{x-2}{x+4} \).

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(x-7)(x+3)}{(x-7)(x-3)} \), we can cancel the common factor \( (x-7) \) from the numerator and denominator, resulting in \( \frac{x+3}{x-3} \). Thus, the correct answer is \( \frac{x+3}{x-3} \).

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(5x+10)(x-1)}{(5x+10)(x+1)} \), we can cancel \( 5x+10 \) from the numerator and denominator (as long as \( 5x+10 \neq 0 \)). This gives us \( \frac{x-1}{x+1} \), which is the correct answer.

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(4x-8)(x+2)}{(4x-8)(x-2)} \), we can cancel the common factor \( 4x-8 \) (as long as \( x \neq 2 \)). This gives us \( \frac{x+2}{x-2} \), which is the correct answer.

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(x^2-9)(x+4)}{(x^2-9)(x-4)} \), we can cancel \( x^2-9 \) from the numerator and denominator (as long as \( x \neq 3 \) and \( x \neq -3 \)). This leaves us with \( \frac{x+4}{x-4} \).

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(6x+12)(x-5)}{(6x+12)(x+3)} \), we can cancel \( 6x+12 \) from the numerator and denominator (as long as \( 6x+12 \neq 0 \)). This gives us \( \frac{x-5}{x+3} \), which is the correct answer.

Tags

CCSS.HSA.APR.D.6