Asked by Katerina Yanushefski on May 20, 2024
Verified
Simplify the rational expression. x2+8xy−9y2x2+10xy+9y2\frac { x ^ { 2 } + 8 x y - 9 y ^ { 2 } } { x ^ { 2 } + 10 x y + 9 y ^ { 2 } }x2+10xy+9y2x2+8xy−9y2
A) x−yx+y,x≠−9y\frac { x - y } { x + y } , x \neq - 9 yx+yx−y,x=−9y
B) x−yx+9y,x≠y\frac { x - y } { x + 9 y } , x \neq yx+9yx−y,x=y
C) x+yx−9y,x≠9y\frac { x + y } { x - 9 y } , x \neq 9 yx−9yx+y,x=9y
D) x+9yx+y,x≠−y\frac { x + 9 y } { x + y } , x \neq - yx+yx+9y,x=−y
E) x−9yx+9y,x≠−9y\frac { x - 9 y } { x + 9 y } , x \neq - 9 yx+9yx−9y,x=−9y
Rational Expression
An expression formed by the quotient of two polynomials, resembling a fraction in which both numerator and denominator are polynomials.
Simplify
The process of altering an expression or equation to its most basic form without changing its value.
- Condense polynomial-based rational expressions.
Verified Answer
TM
Teresa MayfieldMay 24, 2024
Final Answer :
A
Explanation :
Factor the numerator and denominator:
x2+8xy−9y2x2+10xy+9y2=(x−y)(x+9y)(x+y)(x+9y)=x−yx+y,for x≠−9y\begin{align*}\frac{x^2+8xy-9y^2}{x^2+10xy+9y^2}&=\frac{(x- y)(x+9y)}{(x+y)(x+9y)}\\&=\frac{x-y}{x+y},\quad\text{for } x\neq -9y\end{align*}x2+10xy+9y2x2+8xy−9y2=(x+y)(x+9y)(x−y)(x+9y)=x+yx−y,for x=−9y
x2+8xy−9y2x2+10xy+9y2=(x−y)(x+9y)(x+y)(x+9y)=x−yx+y,for x≠−9y\begin{align*}\frac{x^2+8xy-9y^2}{x^2+10xy+9y^2}&=\frac{(x- y)(x+9y)}{(x+y)(x+9y)}\\&=\frac{x-y}{x+y},\quad\text{for } x\neq -9y\end{align*}x2+10xy+9y2x2+8xy−9y2=(x+y)(x+9y)(x−y)(x+9y)=x+yx−y,for x=−9y
Learning Objectives
- Condense polynomial-based rational expressions.
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