Solve 13/xy^2-2y^2/8x^2

$$\frac { 13 } { x y ^ { 2 } } - \frac { 2 y ^ { 2 } } { 8 x ^ { 2 } }$$

Evaluate

$$\frac{52x-y^{4}}{4\left(xy\right)^{2}}$$

Short Solution Steps

Cancel out 2 in both numerator and denominator.

$$\frac{13}{xy^{2}}-\frac{y^{2}}{4x^{2}}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of xy^{2} and 4x^{2} is 4x^{2}y^{2}. Multiply \frac{13}{xy^{2}} times \frac{4x}{4x}. Multiply \frac{y^{2}}{4x^{2}} times \frac{y^{2}}{y^{2}}.

$$\frac{13\times 4x}{4x^{2}y^{2}}-\frac{y^{2}y^{2}}{4x^{2}y^{2}}$$

Since \frac{13\times 4x}{4x^{2}y^{2}} and \frac{y^{2}y^{2}}{4x^{2}y^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{13\times 4x-y^{2}y^{2}}{4x^{2}y^{2}}$$

Do the multiplications in 13\times 4x-y^{2}y^{2}.

$$\frac{52x-y^{4}}{4x^{2}y^{2}}$$

Factor

$$\frac{52x-y^{4}}{4\left(xy\right)^{2}}$$