Asked by Mallory Sheets on May 25, 2024
Verified
Combine and simplify. xx+4−3x−7\frac { x } { x + 4 } - \frac { 3 } { x - 7 }x+4x−x−73
A) x2−10x−12(x+4) (x−7) \frac { x ^ { 2 } - 10 x - 12 } { ( x + 4 ) ( x - 7 ) }(x+4) (x−7) x2−10x−12
B) x(x−11) (x+3) \frac { x ( x - 11 ) } { ( x + 3 ) }(x+3) x(x−11)
C) x(x−7) (x+7) (x−4) \frac { x ( x - 7 ) } { ( x + 7 ) ( x - 4 ) }(x+7) (x−4) x(x−7)
D) x2−7(x+3) (x−4) \frac { x ^ { 2 } - 7 } { ( x + 3 ) ( x - 4 ) }(x+3) (x−4) x2−7
E) x−3(x+4) (x−7) \frac { x - 3 } { ( x + 4 ) ( x - 7 ) }(x+4) (x−7) x−3
Combine
This refers to the process of joining two or more items together, often used in mathematics to sum similar terms.
Simplify
The process of altering an expression into its most basic or concise form, without changing its value.
- Manage the operations of addition and subtraction when dealing with algebraic fractions.
Verified Answer
TS
Twinkle SanghviMay 28, 2024
Final Answer :
A
Explanation :
To combine and simplify the given expression, we need to find a common denominator for the two fractions. The common denominator will be $(x+4)(x-7)$, so we need to rewrite the given fractions with this denominator. We can do this by multiplying the numerator and denominator of the first fraction by $(x-7)$ and the numerator and denominator of the second fraction by $(x+4)$. This gives us: x(x−7)(x+4)(x−7)−3(x+4)(x+4)(x−7)\frac{x(x-7)}{(x+4)(x-7)}-\frac{3(x+4)}{(x+4)(x-7)}(x+4)(x−7)x(x−7)−(x+4)(x−7)3(x+4) Simplifying this expression gives: x(x−7)−3(x+4)(x+4)(x−7)\frac{x(x-7)-3(x+4)}{(x+4)(x-7)}(x+4)(x−7)x(x−7)−3(x+4) Multiplying out the brackets on the numerator gives: x2−7x−3x−12(x+4)(x−7)\frac{x^2-7x-3x-12}{(x+4)(x-7)}(x+4)(x−7)x2−7x−3x−12 Combining like terms on the numerator gives: x2−10x−12(x+4)(x−7)\frac{x^2-10x-12}{(x+4)(x-7)}(x+4)(x−7)x2−10x−12 Therefore, the answer is A.
Learning Objectives
- Manage the operations of addition and subtraction when dealing with algebraic fractions.