Solve x/14a^3+21a^2b:x3/6a^2+9ab

$$\frac { x } { 14 a ^ { 3 } + 21 a ^ { 2 } b } : \frac { x 3 } { 6 a ^ { 2 } + 9 a b }$$

Evaluate

$$\frac{3x}{7ax_{3}}$$

Short Solution Steps

Divide \frac{x}{14a^{3}+21a^{2}b} by \frac{x_{3}}{6a^{2}+9ab} by multiplying \frac{x}{14a^{3}+21a^{2}b} by the reciprocal of \frac{x_{3}}{6a^{2}+9ab}.

$$\frac{x\left(6a^{2}+9ab\right)}{\left(14a^{3}+21a^{2}b\right)x_{3}}$$

Factor the expressions that are not already factored.

$$\frac{3ax\left(2a+3b\right)}{7x_{3}\left(2a+3b\right)a^{2}}$$

Cancel out a\left(2a+3b\right) in both numerator and denominator.

$$\frac{3x}{7ax_{3}}$$

Differentiate w.r.t. x

$$\frac{3}{7ax_{3}}$$