Solve z+3/z+1=z-5/z+9

$$\frac { z + 3 } { z + 1 } = \frac { z - 5 } { z + 9 }$$

Solve for z

$$z=-2$$

Steps for Solving Linear Equation

Variable z 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(z+1\right)\left(z+9\right), the least common multiple of z+1,z+9.

$$\left(z+9\right)\left(z+3\right)=\left(z+1\right)\left(z-5\right)$$

Use the distributive property to multiply z+9 by z+3 and combine like terms.

$$z^{2}+12z+27=\left(z+1\right)\left(z-5\right)$$

Use the distributive property to multiply z+1 by z-5 and combine like terms.

$$z^{2}+12z+27=z^{2}-4z-5$$

Subtract z^{2} from both sides.

$$z^{2}+12z+27-z^{2}=-4z-5$$

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

$$12z+27=-4z-5$$

Add 4z to both sides.

$$12z+27+4z=-5$$

Combine 12z and 4z to get 16z.

$$16z+27=-5$$

Subtract 27 from both sides.

$$16z=-5-27$$

Subtract 27 from -5 to get -32.

$$16z=-32$$

Divide both sides by 16.

$$z=\frac{-32}{16}$$

Divide -32 by 16 to get -2.

$$z=-2$$