Solve 1/y+1+1/y+2=2/y+10

$$\frac{ 1 }{ y+1 } + \frac{ 1 }{ y+2 } = \frac{ 2 }{ y+10 }$$

Solve for y

$$y = -\frac{26}{17} = -1\frac{9}{17} \approx -1.529411765$$

Steps for Solving Linear Equation

Variable y cannot be equal to any of the values -10,-2,-1 since division by zero is not defined. Multiply both sides of the equation by \left(y+1\right)\left(y+2\right)\left(y+10\right), the least common multiple of y+1,y+2,y+10.

$$\left(y+2\right)\left(y+10\right)+\left(y+1\right)\left(y+10\right)=\left(y+1\right)\left(y+2\right)\times 2$$

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

$$y^{2}+12y+20+\left(y+1\right)\left(y+10\right)=\left(y+1\right)\left(y+2\right)\times 2$$

Use the distributive property to multiply y+1 by y+10 and combine like terms.

$$y^{2}+12y+20+y^{2}+11y+10=\left(y+1\right)\left(y+2\right)\times 2$$

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

$$2y^{2}+12y+20+11y+10=\left(y+1\right)\left(y+2\right)\times 2$$

Combine 12y and 11y to get 23y.

$$2y^{2}+23y+20+10=\left(y+1\right)\left(y+2\right)\times 2$$

Add 20 and 10 to get 30.

$$2y^{2}+23y+30=\left(y+1\right)\left(y+2\right)\times 2$$

Use the distributive property to multiply y+1 by y+2 and combine like terms.

$$2y^{2}+23y+30=\left(y^{2}+3y+2\right)\times 2$$

Use the distributive property to multiply y^{2}+3y+2 by 2.

$$2y^{2}+23y+30=2y^{2}+6y+4$$

Subtract 2y^{2} from both sides.

$$2y^{2}+23y+30-2y^{2}=6y+4$$

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

$$23y+30=6y+4$$

Subtract 6y from both sides.

$$23y+30-6y=4$$

Combine 23y and -6y to get 17y.

$$17y+30=4$$

Subtract 30 from both sides.

$$17y=4-30$$

Subtract 30 from 4 to get -26.

$$17y=-26$$

Divide both sides by 17.

$$y=\frac{-26}{17}$$

Fraction \frac{-26}{17} can be rewritten as -\frac{26}{17} by extracting the negative sign.

$$y=-\frac{26}{17}$$