Asked by Nicholas Felix on May 17, 2024
Verified
Simplify the complex fraction. (x2+5x−36x+6) 3x−12\frac { \left( \frac { x ^ { 2 } + 5 x - 36 } { x + 6 } \right) } { 3 x - 12 }3x−12(x+6x2+5x−36)
A) x+93(x+6) ,x≠4\frac { x + 9 } { 3 ( x + 6 ) } , x \neq 43(x+6) x+9,x=4
B) x−93(x+6) ,x≠−4\frac { x - 9 } { 3 ( x + 6 ) } , x \neq - 43(x+6) x−9,x=−4
C) x−43(x−9) ,x≠−4\frac { x - 4 } { 3 ( x - 9 ) } , x \neq - 43(x−9) x−4,x=−4
D) x+63(x−4) ,x≠4\frac { x + 6 } { 3 ( x - 4 ) } , x \neq 43(x−4) x+6,x=4
E) x+43(x+9) ,x≠4\frac { x + 4 } { 3 ( x + 9 ) } , x \neq 43(x+9) x+4,x=4
Complex Fraction
A fraction where the numerator, denominator, or both contain a fraction.
Simplify
Simplifying involves reducing an expression or equation to its most basic form, making it easier to work with.
- Acquire the ability to simplify complex fractions through a defined method.
Verified Answer
GD
gwendolyn dukesMay 21, 2024
Final Answer :
A
Explanation :
First, factor the numerator and denominator where possible. The numerator x2+5x−36x+6\frac{x^2 + 5x - 36}{x + 6}x+6x2+5x−36 simplifies to (x+9)(x−4)x+6\frac{(x + 9)(x - 4)}{x + 6}x+6(x+9)(x−4) after factoring x2+5x−36x^2 + 5x - 36x2+5x−36 . The denominator 3x−123x - 123x−12 simplifies to 3(x−4)3(x - 4)3(x−4) after factoring out the 3. Thus, the complex fraction simplifies to x+93(x+6)\frac{x + 9}{3(x + 6)}3(x+6)x+9 , with the condition x≠4x \neq 4x=4 to avoid division by zero in the original denominator.
Learning Objectives
- Acquire the ability to simplify complex fractions through a defined method.