Solve y+5/y+2=y+10/y+6

$$\frac { y + 5 } { y + 2 } = \frac { y + 10 } { y + 6 }$$

Solve for y

$$y=10$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -6,-2 since division by zero is not defined. Multiply both sides of the equation by \left(y+2\right)\left(y+6\right), the least common multiple of y+2,y+6.

$$\left(y+6\right)\left(y+5\right)=\left(y+2\right)\left(y+10\right)$$

Use the distributive property to multiply y+6 by y+5 and combine like terms.

$$y^{2}+11y+30=\left(y+2\right)\left(y+10\right)$$

Use the distributive property to multiply y+2 by y+10 and combine like terms.

$$y^{2}+11y+30=y^{2}+12y+20$$

Subtract y^{2} from both sides.

$$y^{2}+11y+30-y^{2}=12y+20$$

Combine y^{2} and -y^{2} to get 0.

$$11y+30=12y+20$$

Subtract 12y from both sides.

$$11y+30-12y=20$$

Combine 11y and -12y to get -y.

$$-y+30=20$$

Subtract 30 from both sides.

$$-y=20-30$$

Subtract 30 from 20 to get -10.

$$-y=-10$$

Multiply both sides by -1.

$$y=10$$