Solve 2y+8/y^2-4y+4-7/y-2quad3)

$$\frac { 2 y + 8 } { y ^ { 2 } - 4 y + 4 } - \frac { 7 } { y - 2 } \quad 3 )$$

Evaluate

$$\frac{50-19y}{\left(y-2\right)^{2}}$$

Short Solution Steps

Express \frac{7}{y-2}\times 3 as a single fraction.

$$\frac{2y+8}{y^{2}-4y+4}-\frac{7\times 3}{y-2}$$

Multiply 7 and 3 to get 21.

$$\frac{2y+8}{y^{2}-4y+4}-\frac{21}{y-2}$$

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

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{21}{y-2}$$

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{21}{y-2} times \frac{y-2}{y-2}.

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{21\left(y-2\right)}{\left(y-2\right)^{2}}$$

Since \frac{2y+8}{\left(y-2\right)^{2}} and \frac{21\left(y-2\right)}{\left(y-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2y+8-21\left(y-2\right)}{\left(y-2\right)^{2}}$$

Do the multiplications in 2y+8-21\left(y-2\right).

$$\frac{2y+8-21y+42}{\left(y-2\right)^{2}}$$

Combine like terms in 2y+8-21y+42.

$$\frac{-19y+50}{\left(y-2\right)^{2}}$$

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

$$\frac{-19y+50}{y^{2}-4y+4}$$

Expand

$$\frac{50-19y}{\left(y-2\right)^{2}}$$

Short Solution Steps

Express \frac{7}{y-2}\times 3 as a single fraction.

$$\frac{2y+8}{y^{2}-4y+4}-\frac{7\times 3}{y-2}$$

Multiply 7 and 3 to get 21.

$$\frac{2y+8}{y^{2}-4y+4}-\frac{21}{y-2}$$

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

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{21}{y-2}$$

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{21}{y-2} times \frac{y-2}{y-2}.

$$\frac{2y+8}{\left(y-2\right)^{2}}-\frac{21\left(y-2\right)}{\left(y-2\right)^{2}}$$

Since \frac{2y+8}{\left(y-2\right)^{2}} and \frac{21\left(y-2\right)}{\left(y-2\right)^{2}} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2y+8-21\left(y-2\right)}{\left(y-2\right)^{2}}$$

Do the multiplications in 2y+8-21\left(y-2\right).

$$\frac{2y+8-21y+42}{\left(y-2\right)^{2}}$$

Combine like terms in 2y+8-21y+42.

$$\frac{-19y+50}{\left(y-2\right)^{2}}$$

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

$$\frac{-19y+50}{y^{2}-4y+4}$$