Solve 3/7(x+1)^frac{7{3}}+3(x+1)^frac{4{3}}

$$\frac { 3 } { 7 } ( x + 1 ) ^ { \frac { 7 } { 3 } } + 3 ( x + 1 ) ^ { \frac { 4 } { 3 } }$$

Factor

$$\frac{3\left(x+8\right)\left(x+1\right)^{\frac{4}{3}}}{7}$$

Solution Steps

Factor out \frac{3}{7}.

$$\frac{3\left(\left(x+1\right)^{\frac{7}{3}}+7\left(x+1\right)^{\frac{4}{3}}\right)}{7}$$

Consider \left(x+1\right)^{\frac{7}{3}}+7\left(x+1\right)^{\frac{4}{3}}. Factor out \left(x+1\right)^{\frac{4}{3}}.

$$\left(x+1\right)^{\frac{4}{3}}\left(x+8\right)$$

Consider x+1+7. Multiply and combine like terms.

$$x+8$$

Rewrite the complete factored expression.

$$\frac{3\left(x+1\right)^{\frac{4}{3}}\left(x+8\right)}{7}$$

Evaluate

$$\frac{3\left(x+8\right)\left(x+1\right)^{\frac{4}{3}}}{7}$$