Perform the indicated operations.
-$$\frac { 5 x ^ { 2 } + 38 x - 63 } { 2 x - 18 } \cdot \frac { x ^ { 2 } - 9 x } { 25 x ^ { 2 } - 49 } \div \frac { 6 x + 54 } { 7 x ^ { 3 } }$$
A) $\frac { 7 x ^ { 4 } } { 12 ( 5 x + 7 ) }$
B) $\frac { 6 ( x + 9 ) ^ { 2 } } { 14 x ^ { 2 } ( 5 x + 7 ) }$
C) $\frac { 7 x ^ { 3 } } { 12 ( 5 x + 7 ) }$
D) $\frac { 12 } { 7 x ^ { 4 } ( 5 x + 7 ) }$

Question

Quizplus · Accepted Answer

First, factorize each polynomial where possible and simplify the expression. The numerator of the first fraction $\frac{5x^2 + 38x - 63}{2x - 18}$ can be factored as $(5x - 7)(x + 9)$, and the denominator can be written as $2(x - 9)$. The second fraction $\frac{x^2 - 9x}{25x^2 - 49}$ can be simplified by factoring the numerator as $x(x - 9)$ and the denominator as $(5x + 7)(5x - 7)$. The division by $\frac{6x + 54}{7x^3}$ can be turned into multiplication by its reciprocal, which simplifies to $\frac{7x^3}{6(x + 9)}$. After canceling out common factors across the entire expression, we are left with $\frac{7x^4}{12(5x + 7)}$, which matches option A.

Perform the Indicated Operations 5x2+38x−632x−18⋅x2−9x25x2−49÷6x+547x3\frac { 5 x ^ { 2 } + 38 x - 63 } { 2 x - 18 } \cdot \frac { x ^ { 2 } - 9 x } { 25 x ^ { 2 } - 49 } \div \frac { 6 x + 54 } { 7 x ^ { 3 } }2x−185x2+38x−63​⋅25x2−49x2−9x​÷7x36x+54​

Perform the Indicated Operations $\frac { 5 x ^ { 2 } + 38 x - 63 } { 2 x - 18 } \cdot \frac { x ^ { 2 } - 9 x } { 25 x ^ { 2 } - 49 } \div \frac { 6 x + 54 } { 7 x ^ { 3 } }$