Solve frac{4x^{2}-y^{2}}{2x^{2}+xy-y^{2}}div6x^2+7xy+2y^2/3x^2+5xy+2y^2

$$\frac { 4 x ^ { 2 } - y ^ { 2 } } { 2 x ^ { 2 } + x y - y ^ { 2 } } \div \frac { 6 x ^ { 2 } + 7 x y + 2 y ^ { 2 } } { 3 x ^ { 2 } + 5 x y + 2 y ^ { 2 } }$$

Evaluate

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Short Solution Steps

Divide \frac{4x^{2}-y^{2}}{2x^{2}+xy-y^{2}} by \frac{6x^{2}+7xy+2y^{2}}{3x^{2}+5xy+2y^{2}} by multiplying \frac{4x^{2}-y^{2}}{2x^{2}+xy-y^{2}} by the reciprocal of \frac{6x^{2}+7xy+2y^{2}}{3x^{2}+5xy+2y^{2}}.

$$\frac{\left(4x^{2}-y^{2}\right)\left(3x^{2}+5xy+2y^{2}\right)}{\left(2x^{2}+xy-y^{2}\right)\left(6x^{2}+7xy+2y^{2}\right)}$$

Factor the expressions that are not already factored.

$$\frac{\left(x+y\right)\left(2x+y\right)\left(2x-y\right)\left(3x+2y\right)}{\left(x+y\right)\left(2x+y\right)\left(2x-y\right)\left(3x+2y\right)}$$

Cancel out \left(x+y\right)\left(2x+y\right)\left(2x-y\right)\left(3x+2y\right) in both numerator and denominator.

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Factor

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