Perform the operation indicated.
-$\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }$
A) $\frac { 5 x } { 4 }$
B) $\frac { 5 x } { 12 }$
C) $\frac { x } { 4 }$
D) $\frac { 5 } { 4 }$

Question

Quizplus · Accepted Answer

First, simplify the fractions by factoring out common terms. The first fraction $\frac{3x}{6x+3}$ can be simplified by factoring out a 3 from the denominator, giving $\frac{3x}{3(2x+1)}$, which simplifies to $\frac{x}{2x+1}$. The second fraction $\frac{10x+5}{4}$ can be simplified by factoring out a 5 from the numerator, giving $\frac{5(2x+1)}{4}$. Multiplying these simplified fractions $\frac{x}{2x+1} \cdot \frac{5(2x+1)}{4}$ allows the $2x+1$ terms to cancel out, leaving $\frac{5x}{4}$.

Perform the Operation Indicated 3x6x+3⋅10x+54\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }6x+33x​⋅410x+5​

Perform the Operation Indicated $\frac { 3 x } { 6 x + 3 } \cdot \frac { 10 x + 5 } { 4 }$