Solve 3y/(8y+9)(2y-3)-y^2/(8y-7)(2y-3)=

$$\frac { 3 y } { ( 8 y + 9 ) ( 2 y - 3 ) } - \frac { y ^ { 2 } } { ( 8 y - 7 ) ( 2 y - 3 ) } =$$

Evaluate

$$\frac{y\left(-8y^{2}+15y-21\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(8y+9\right)\left(2y-3\right) and \left(8y-7\right)\left(2y-3\right) is \left(2y-3\right)\left(8y-7\right)\left(8y+9\right). Multiply \frac{3y}{\left(8y+9\right)\left(2y-3\right)} times \frac{8y-7}{8y-7}. Multiply \frac{y^{2}}{\left(8y-7\right)\left(2y-3\right)} times \frac{8y+9}{8y+9}.

$$\frac{3y\left(8y-7\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}-\frac{y^{2}\left(8y+9\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Since \frac{3y\left(8y-7\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)} and \frac{y^{2}\left(8y+9\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3y\left(8y-7\right)-y^{2}\left(8y+9\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Do the multiplications in 3y\left(8y-7\right)-y^{2}\left(8y+9\right).

$$\frac{24y^{2}-21y-8y^{3}-9y^{2}}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Combine like terms in 24y^{2}-21y-8y^{3}-9y^{2}.

$$\frac{15y^{2}-21y-8y^{3}}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Expand \left(2y-3\right)\left(8y-7\right)\left(8y+9\right).

$$\frac{15y^{2}-21y-8y^{3}}{128y^{3}-160y^{2}-174y+189}$$

Expand

$$\frac{-8y^{3}+15y^{2}-21y}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(8y+9\right)\left(2y-3\right) and \left(8y-7\right)\left(2y-3\right) is \left(2y-3\right)\left(8y-7\right)\left(8y+9\right). Multiply \frac{3y}{\left(8y+9\right)\left(2y-3\right)} times \frac{8y-7}{8y-7}. Multiply \frac{y^{2}}{\left(8y-7\right)\left(2y-3\right)} times \frac{8y+9}{8y+9}.

$$\frac{3y\left(8y-7\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}-\frac{y^{2}\left(8y+9\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Since \frac{3y\left(8y-7\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)} and \frac{y^{2}\left(8y+9\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{3y\left(8y-7\right)-y^{2}\left(8y+9\right)}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Do the multiplications in 3y\left(8y-7\right)-y^{2}\left(8y+9\right).

$$\frac{24y^{2}-21y-8y^{3}-9y^{2}}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Combine like terms in 24y^{2}-21y-8y^{3}-9y^{2}.

$$\frac{15y^{2}-21y-8y^{3}}{\left(2y-3\right)\left(8y-7\right)\left(8y+9\right)}$$

Expand \left(2y-3\right)\left(8y-7\right)\left(8y+9\right).

$$\frac{15y^{2}-21y-8y^{3}}{128y^{3}-160y^{2}-174y+189}$$