Asked by Cally Harlin on May 10, 2024
Verified
Multiply and simplify. (4x−9) (x+9) x6⋅x9−4x\frac { ( 4 x - 9 ) ( x + 9 ) } { x ^ { 6 } } \cdot \frac { x } { 9 - 4 x }x6(4x−9) (x+9) ⋅9−4xx
A) 3249−4x,x≠49\frac { 324 } { 9 - 4 x } , x \neq \frac { 4 } { 9 }9−4x324,x=94
B) x−9x6,x≠−9\frac { x - 9 } { x ^ { 6 } } , x \neq - 9x6x−9,x=−9
C) −x+9x5,x≠94- \frac { x + 9 } { x ^ { 5 } } , x \neq \frac { 9 } { 4 }−x5x+9,x=49
D) −x+9x7,x≠−49- \frac { x + 9 } { x ^ { 7 } } , x \neq - \frac { 4 } { 9 }−x7x+9,x=−94
E) (4x−9) (x+9) 36,x≠−94\frac { ( 4 x - 9 ) ( x + 9 ) } { 36 } , x \neq - \frac { 9 } { 4 }36(4x−9) (x+9) ,x=−49
Multiply
The mathematical operation of increasing a number by another specified number of times, essentially repeated addition.
- Perform multiplicative and divisive functions on algebraic fractions.
Verified Answer
CB
Chelsey BullockMay 15, 2024
Final Answer :
C
Explanation :
First, we need to simplify the expression:
(4x−9)(x+9)x6⋅x9−4x=(4x−9)(x+9)xx6(9−4x)=(4x−9)(x+9)xx5(x−9)=(4x−9)(x+9)x4(x−9).\frac{(4x-9)(x+9)}{x^6}\cdot\frac{x}{9-4x}=\frac{(4x-9)(x+9)x}{x^6(9-4x)}=\frac{(4x-9)(x+9)x}{x^5(x-9)}=\frac{(4x-9)(x+9)}{x^4(x-9)}.x6(4x−9)(x+9)⋅9−4xx=x6(9−4x)(4x−9)(x+9)x=x5(x−9)(4x−9)(x+9)x=x4(x−9)(4x−9)(x+9).
Next, we need to simplify the expression further by factoring the numerator:
(4x−9)(x+9)x4(x−9)=(4x−9)⋅32x4(x−9)=32(4x−9)x4(9−4x).\frac{(4x-9)(x+9)}{x^4(x-9)}=\frac{(4x-9)\cdot 3^2}{x^4(x-9)}=\frac{3^2(4x-9)}{x^4(9-4x)}.x4(x−9)(4x−9)(x+9)=x4(x−9)(4x−9)⋅32=x4(9−4x)32(4x−9).
The final simplified expression has the same denominator as the original expression, but the numerator is different. Therefore, option C, $-\frac{x+9}{x^5},$ cannot be correct. The correct answer is option A, $\frac{324}{9-4x},$ since it has the same denominator and simplified numerator. However, we need to add the restriction $x\neq\frac{9}{4}$ due to the denominator of the second fraction in the original expression.
(4x−9)(x+9)x6⋅x9−4x=(4x−9)(x+9)xx6(9−4x)=(4x−9)(x+9)xx5(x−9)=(4x−9)(x+9)x4(x−9).\frac{(4x-9)(x+9)}{x^6}\cdot\frac{x}{9-4x}=\frac{(4x-9)(x+9)x}{x^6(9-4x)}=\frac{(4x-9)(x+9)x}{x^5(x-9)}=\frac{(4x-9)(x+9)}{x^4(x-9)}.x6(4x−9)(x+9)⋅9−4xx=x6(9−4x)(4x−9)(x+9)x=x5(x−9)(4x−9)(x+9)x=x4(x−9)(4x−9)(x+9).
Next, we need to simplify the expression further by factoring the numerator:
(4x−9)(x+9)x4(x−9)=(4x−9)⋅32x4(x−9)=32(4x−9)x4(9−4x).\frac{(4x-9)(x+9)}{x^4(x-9)}=\frac{(4x-9)\cdot 3^2}{x^4(x-9)}=\frac{3^2(4x-9)}{x^4(9-4x)}.x4(x−9)(4x−9)(x+9)=x4(x−9)(4x−9)⋅32=x4(9−4x)32(4x−9).
The final simplified expression has the same denominator as the original expression, but the numerator is different. Therefore, option C, $-\frac{x+9}{x^5},$ cannot be correct. The correct answer is option A, $\frac{324}{9-4x},$ since it has the same denominator and simplified numerator. However, we need to add the restriction $x\neq\frac{9}{4}$ due to the denominator of the second fraction in the original expression.
Learning Objectives
- Perform multiplicative and divisive functions on algebraic fractions.