Solve 2y+8/y^2-4y+4-7/y-2

$$\frac{ 2y+8 }{ { y }^{ 2 } -4y+4 } - \frac{ 7 }{ y-2 }$$

Evaluate

$$\frac{22-5y}{\left(y-2\right)^{2}}$$

Short Solution Steps

Factor y^{2}-4y+4.

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{7}{y-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(y-2\right)^{2} and y-2 is \left(y-2\right)^{2}. Multiply \frac{7}{y-2} times \frac{y-2}{y-2}.

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{7\left(y-2\right)}{\left(y-2\right)^{2}}$$

Since \frac{2y+8}{\left(y-2\right)^{2}} and \frac{7\left(y-2\right)}{\left(y-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2y+8-7\left(y-2\right)}{\left(y-2\right)^{2}}$$

Do the multiplications in 2y+8-7\left(y-2\right).

$$\frac{2y+8-7y+14}{\left(y-2\right)^{2}}$$

Combine like terms in 2y+8-7y+14.

$$\frac{-5y+22}{\left(y-2\right)^{2}}$$

Expand \left(y-2\right)^{2}.

$$\frac{-5y+22}{y^{2}-4y+4}$$

Expand

$$\frac{22-5y}{\left(y-2\right)^{2}}$$

Short Solution Steps

Factor y^{2}-4y+4.

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{7}{y-2}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of \left(y-2\right)^{2} and y-2 is \left(y-2\right)^{2}. Multiply \frac{7}{y-2} times \frac{y-2}{y-2}.

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{7\left(y-2\right)}{\left(y-2\right)^{2}}$$

Since \frac{2y+8}{\left(y-2\right)^{2}} and \frac{7\left(y-2\right)}{\left(y-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2y+8-7\left(y-2\right)}{\left(y-2\right)^{2}}$$

Do the multiplications in 2y+8-7\left(y-2\right).

$$\frac{2y+8-7y+14}{\left(y-2\right)^{2}}$$

Combine like terms in 2y+8-7y+14.

$$\frac{-5y+22}{\left(y-2\right)^{2}}$$

Expand \left(y-2\right)^{2}.

$$\frac{-5y+22}{y^{2}-4y+4}$$