Solve x^2-2y-35div6y-30/y^2-25

$$x ^ { 2 } - 2 y - 35 \div \frac { 6 y - 30 } { y ^ { 2 } - 25 }$$

Evaluate

$$x^{2}-\frac{47y}{6}-\frac{175}{6}$$

$$|y|\neq 5$$

Short Solution Steps

Divide 35 by \frac{6y-30}{y^{2}-25} by multiplying 35 by the reciprocal of \frac{6y-30}{y^{2}-25}.

$$x^{2}-2y-\frac{35\left(y^{2}-25\right)}{6y-30}$$

Factor the expressions that are not already factored in \frac{35\left(y^{2}-25\right)}{6y-30}.

$$x^{2}-2y-\frac{35\left(y-5\right)\left(y+5\right)}{6\left(y-5\right)}$$

Cancel out y-5 in both numerator and denominator.

$$x^{2}-2y-\frac{35\left(y+5\right)}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-2y times \frac{6}{6}.

$$\frac{6\left(x^{2}-2y\right)}{6}-\frac{35\left(y+5\right)}{6}$$

Since \frac{6\left(x^{2}-2y\right)}{6} and \frac{35\left(y+5\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\left(x^{2}-2y\right)-35\left(y+5\right)}{6}$$

Do the multiplications in 6\left(x^{2}-2y\right)-35\left(y+5\right).

$$\frac{6x^{2}-12y-35y-175}{6}$$

Combine like terms in 6x^{2}-12y-35y-175.

$$\frac{6x^{2}-47y-175}{6}$$

Expand

$$x^{2}-\frac{47y}{6}-\frac{175}{6}$$

$$|y|\neq 5$$

Short Solution Steps

Divide 35 by \frac{6y-30}{y^{2}-25} by multiplying 35 by the reciprocal of \frac{6y-30}{y^{2}-25}.

$$x^{2}-2y-\frac{35\left(y^{2}-25\right)}{6y-30}$$

Factor the expressions that are not already factored in \frac{35\left(y^{2}-25\right)}{6y-30}.

$$x^{2}-2y-\frac{35\left(y-5\right)\left(y+5\right)}{6\left(y-5\right)}$$

Cancel out y-5 in both numerator and denominator.

$$x^{2}-2y-\frac{35\left(y+5\right)}{6}$$

To add or subtract expressions, expand them to make their denominators the same. Multiply x^{2}-2y times \frac{6}{6}.

$$\frac{6\left(x^{2}-2y\right)}{6}-\frac{35\left(y+5\right)}{6}$$

Since \frac{6\left(x^{2}-2y\right)}{6} and \frac{35\left(y+5\right)}{6} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\left(x^{2}-2y\right)-35\left(y+5\right)}{6}$$

Do the multiplications in 6\left(x^{2}-2y\right)-35\left(y+5\right).

$$\frac{6x^{2}-12y-35y-175}{6}$$

Combine like terms in 6x^{2}-12y-35y-175.

$$\frac{6x^{2}-47y-175}{6}$$