Simplify/Multiply/Divide Rational Expressions

My first step will be to change the operator to multiplication and reciprocate the second fraction when...

• Adding
• Subtracting
• Multiplying
• Dividing

Tags

CCSS.7.NS.A.2A

To simplify a rational expression, I should

• Eliminate common terms in the numerator and denominator.
• Combine like terms in the numerator and denominator.
• Factor the numerator and denominator and eliminate common factors.
• Find an LCD.

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

Answer explanation

The expression simplifies by canceling the common factor \(x^2-16\) in the numerator and denominator, resulting in \(\frac{x+7}{x-7}\). Thus, the correct answer is \(\frac{x+7}{x-7}\).

Tags

CCSS.HSA.APR.D.6

Answer explanation

To simplify \( \frac{(3x-9)(x+6)}{(3x-9)(x-6)} \), we can cancel the common factor \( (3x-9) \) from the numerator and denominator, resulting in \( \frac{x+6}{x-6} \). Thus, the correct answer is \( \frac{x+6}{x-6} \).

Tags

CCSS.HSA.APR.D.6

Tags

CCSS.HSA.APR.D.6

Tags

CCSS.HSA.APR.D.7

Assuming no denominator is equal to zero, which is equivalent to the following expression?

• 
• 
• 
• 

Tags

CCSS.HSA.APR.D.6