Solve -6y^2/8y+5+3/y^4

$$\frac { - 6 y ^ { 2 } } { 8 y + 5 } + \frac { 3 } { y ^ { 4 } }$$

Evaluate

$$-\frac{6y^{2}}{8y+5}+\frac{3}{y^{4}}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 8y+5 and y^{4} is \left(8y+5\right)y^{4}. Multiply \frac{-6y^{2}}{8y+5} times \frac{y^{4}}{y^{4}}. Multiply \frac{3}{y^{4}} times \frac{8y+5}{8y+5}.

$$\frac{-6y^{2}y^{4}}{\left(8y+5\right)y^{4}}+\frac{3\left(8y+5\right)}{\left(8y+5\right)y^{4}}$$

Since \frac{-6y^{2}y^{4}}{\left(8y+5\right)y^{4}} and \frac{3\left(8y+5\right)}{\left(8y+5\right)y^{4}} have the same denominator, add them by adding their numerators.

$$\frac{-6y^{2}y^{4}+3\left(8y+5\right)}{\left(8y+5\right)y^{4}}$$

Do the multiplications in -6y^{2}y^{4}+3\left(8y+5\right).

$$\frac{-6y^{6}+24y+15}{\left(8y+5\right)y^{4}}$$

Expand \left(8y+5\right)y^{4}.

$$\frac{-6y^{6}+24y+15}{8y^{5}+5y^{4}}$$

Factor

$$\frac{3\left(-\frac{2y^{6}}{8y+5}+1\right)}{y^{4}}$$