Solve frac{6a^{2}+19ab-7b^{2}}{6a^{2}-5ab+b^{2}}div2a^2+13ab+21b^2/14a^2-ab-3b^2=

$$\frac { 6 a ^ { 2 } + 19 a b - 7 b ^ { 2 } } { 6 a ^ { 2 } - 5 a b + b ^ { 2 } } \div \frac { 2 a ^ { 2 } + 13 a b + 21 b ^ { 2 } } { 14 a ^ { 2 } - a b - 3 b ^ { 2 } } =$$

Evaluate

$$\frac{7a+3b}{a+3b}$$

Short Solution Steps

Divide \frac{6a^{2}+19ab-7b^{2}}{6a^{2}-5ab+b^{2}} by \frac{2a^{2}+13ab+21b^{2}}{14a^{2}-ab-3b^{2}} by multiplying \frac{6a^{2}+19ab-7b^{2}}{6a^{2}-5ab+b^{2}} by the reciprocal of \frac{2a^{2}+13ab+21b^{2}}{14a^{2}-ab-3b^{2}}.

$$\frac{\left(6a^{2}+19ab-7b^{2}\right)\left(14a^{2}-ab-3b^{2}\right)}{\left(6a^{2}-5ab+b^{2}\right)\left(2a^{2}+13ab+21b^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2a-b\right)\left(3a-b\right)\left(2a+7b\right)\left(7a+3b\right)}{\left(a+3b\right)\left(2a-b\right)\left(3a-b\right)\left(2a+7b\right)}$$

Cancel out \left(2a-b\right)\left(3a-b\right)\left(2a+7b\right) in both numerator and denominator.

$$\frac{7a+3b}{a+3b}$$

Expand

$$\frac{7a+3b}{a+3b}$$

Short Solution Steps

Divide \frac{6a^{2}+19ab-7b^{2}}{6a^{2}-5ab+b^{2}} by \frac{2a^{2}+13ab+21b^{2}}{14a^{2}-ab-3b^{2}} by multiplying \frac{6a^{2}+19ab-7b^{2}}{6a^{2}-5ab+b^{2}} by the reciprocal of \frac{2a^{2}+13ab+21b^{2}}{14a^{2}-ab-3b^{2}}.

$$\frac{\left(6a^{2}+19ab-7b^{2}\right)\left(14a^{2}-ab-3b^{2}\right)}{\left(6a^{2}-5ab+b^{2}\right)\left(2a^{2}+13ab+21b^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(2a-b\right)\left(3a-b\right)\left(2a+7b\right)\left(7a+3b\right)}{\left(a+3b\right)\left(2a-b\right)\left(3a-b\right)\left(2a+7b\right)}$$

Cancel out \left(2a-b\right)\left(3a-b\right)\left(2a+7b\right) in both numerator and denominator.

$$\frac{7a+3b}{a+3b}$$