Solve y-1/4y+9+9/(4y+9)^2

$$\frac { y - 1 } { 4 y + 9 } + \frac { 9 } { ( 4 y + 9 ) ^ { 2 } }$$

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4y+9 and \left(4y+9\right)^{2} is \left(4y+9\right)^{2}. Multiply \frac{y-1}{4y+9} times \frac{4y+9}{4y+9}.

$$\frac{\left(y-1\right)\left(4y+9\right)}{\left(4y+9\right)^{2}}+\frac{9}{\left(4y+9\right)^{2}}$$

Since \frac{\left(y-1\right)\left(4y+9\right)}{\left(4y+9\right)^{2}} and \frac{9}{\left(4y+9\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(y-1\right)\left(4y+9\right)+9}{\left(4y+9\right)^{2}}$$

Do the multiplications in \left(y-1\right)\left(4y+9\right)+9.

$$\frac{4y^{2}+9y-4y-9+9}{\left(4y+9\right)^{2}}$$

Combine like terms in 4y^{2}+9y-4y-9+9.

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

Expand \left(4y+9\right)^{2}.

$$\frac{4y^{2}+5y}{16y^{2}+72y+81}$$

Expand

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of 4y+9 and \left(4y+9\right)^{2} is \left(4y+9\right)^{2}. Multiply \frac{y-1}{4y+9} times \frac{4y+9}{4y+9}.

$$\frac{\left(y-1\right)\left(4y+9\right)}{\left(4y+9\right)^{2}}+\frac{9}{\left(4y+9\right)^{2}}$$

Since \frac{\left(y-1\right)\left(4y+9\right)}{\left(4y+9\right)^{2}} and \frac{9}{\left(4y+9\right)^{2}} have the same denominator, add them by adding their numerators.

$$\frac{\left(y-1\right)\left(4y+9\right)+9}{\left(4y+9\right)^{2}}$$

Do the multiplications in \left(y-1\right)\left(4y+9\right)+9.

$$\frac{4y^{2}+9y-4y-9+9}{\left(4y+9\right)^{2}}$$

Combine like terms in 4y^{2}+9y-4y-9+9.

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

Expand \left(4y+9\right)^{2}.

$$\frac{4y^{2}+5y}{16y^{2}+72y+81}$$