Solve u+10/u+1=u-6/u+9

$$\frac { u + 10 } { u + 1 } = \frac { u - 6 } { u + 9 }$$

Solve for u

$$u=-4$$

Steps for Solving Linear Equation

Variable u cannot be equal to any of the values -9,-1 since division by zero is not defined. Multiply both sides of the equation by \left(u+1\right)\left(u+9\right), the least common multiple of u+1,u+9.

$$\left(u+9\right)\left(u+10\right)=\left(u+1\right)\left(u-6\right)$$

Use the distributive property to multiply u+9 by u+10 and combine like terms.

$$u^{2}+19u+90=\left(u+1\right)\left(u-6\right)$$

Use the distributive property to multiply u+1 by u-6 and combine like terms.

$$u^{2}+19u+90=u^{2}-5u-6$$

Subtract u^{2} from both sides.

$$u^{2}+19u+90-u^{2}=-5u-6$$

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

$$19u+90=-5u-6$$

Add 5u to both sides.

$$19u+90+5u=-6$$

Combine 19u and 5u to get 24u.

$$24u+90=-6$$

Subtract 90 from both sides.

$$24u=-6-90$$

Subtract 90 from -6 to get -96.

$$24u=-96$$

Divide both sides by 24.

$$u=\frac{-96}{24}$$

Divide -96 by 24 to get -4.

$$u=-4$$