Solve 9y/4y+5+8y^2/6y+5=

$$\frac { 9 y } { 4 y + 5 } + \frac { 8 y ^ { 2 } } { 6 y + 5 } =$$

Evaluate

$$\frac{y\left(32y^{2}+94y+45\right)}{\left(4y+5\right)\left(6y+5\right)}$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4y+5 and 6y+5 is \left(4y+5\right)\left(6y+5\right). Multiply \frac{9y}{4y+5} times \frac{6y+5}{6y+5}. Multiply \frac{8y^{2}}{6y+5} times \frac{4y+5}{4y+5}.

$$\frac{9y\left(6y+5\right)}{\left(4y+5\right)\left(6y+5\right)}+\frac{8y^{2}\left(4y+5\right)}{\left(4y+5\right)\left(6y+5\right)}$$

Since \frac{9y\left(6y+5\right)}{\left(4y+5\right)\left(6y+5\right)} and \frac{8y^{2}\left(4y+5\right)}{\left(4y+5\right)\left(6y+5\right)} have the same denominator, add them by adding their numerators.

$$\frac{9y\left(6y+5\right)+8y^{2}\left(4y+5\right)}{\left(4y+5\right)\left(6y+5\right)}$$

Do the multiplications in 9y\left(6y+5\right)+8y^{2}\left(4y+5\right).

$$\frac{54y^{2}+45y+32y^{3}+40y^{2}}{\left(4y+5\right)\left(6y+5\right)}$$

Combine like terms in 54y^{2}+45y+32y^{3}+40y^{2}.

$$\frac{94y^{2}+45y+32y^{3}}{\left(4y+5\right)\left(6y+5\right)}$$

Expand \left(4y+5\right)\left(6y+5\right).

$$\frac{94y^{2}+45y+32y^{3}}{24y^{2}+50y+25}$$

Factor

$$\frac{32y\left(y-\frac{-\sqrt{769}-47}{32}\right)\left(y-\frac{\sqrt{769}-47}{32}\right)}{\left(4y+5\right)\left(6y+5\right)}$$