Divide Rational Expressions
-$$\frac { 5 x ^ { 2 } + 6 x - 8 } { 2 x - 6 } \cdot \frac { x ^ { 2 } - 3 x } { 25 x ^ { 2 } - 16 } \div \frac { 4 x + 8 } { 3 x ^ { 3 } }$$

Question

Quizplus · Accepted Answer

To solve the given expression, first, simplify and factor each part where possible. The division of rational expressions can be turned into multiplication by flipping the divisor. Factoring gives: $\frac{(5x^2 + 6x - 8)}{(2x - 6)} \cdot \frac{(x^2 - 3x)}{(25x^2 - 16)} \cdot \frac{(3x^3)}{(4x + 8)}$. Factoring further, we get $\frac{(5x + 4)(x - 2)}{2(x - 3)} \cdot \frac{x(x - 3)}{(5x + 4)(5x - 4)} \cdot \frac{3x^3}{4(x + 2)}$. Simplifying, many terms cancel out, leaving $\frac{3x^4}{8(5x + 4)}$, which matches choice A.

Divide Rational Expressions - 5x2+6x−82x−6⋅x2−3x25x2−16÷4x+83x3\frac { 5 x ^ { 2 } + 6 x - 8 } { 2 x - 6 } \cdot \frac { x ^ { 2 } - 3 x } { 25 x ^ { 2 } - 16 } \div \frac { 4 x + 8 } { 3 x ^ { 3 } }2x−65x2+6x−8​⋅25x2−16x2−3x​÷3x34x+8​

Divide Rational Expressions
- $\frac { 5 x ^ { 2 } + 6 x - 8 } { 2 x - 6 } \cdot \frac { x ^ { 2 } - 3 x } { 25 x ^ { 2 } - 16 } \div \frac { 4 x + 8 } { 3 x ^ { 3 } }$