Solve 4/z+1/z=2/z+3

$$\frac { 4 } { z } + \frac { 1 } { z } = \frac { 2 } { z + 3 }$$

Solve for z

$$z=-5$$

Steps for Solving Linear Equation

Variable z cannot be equal to any of the values -3,0 since division by zero is not defined. Multiply both sides of the equation by z\left(z+3\right), the least common multiple of z,z+3.

$$\left(z+3\right)\times 4+z+3=z\times 2$$

Use the distributive property to multiply z+3 by 4.

$$4z+12+z+3=z\times 2$$

Combine 4z and z to get 5z.

$$5z+12+3=z\times 2$$

Add 12 and 3 to get 15.

$$5z+15=z\times 2$$

Subtract z\times 2 from both sides.

$$5z+15-z\times 2=0$$

Combine 5z and -z\times 2 to get 3z.

$$3z+15=0$$

Subtract 15 from both sides. Anything subtracted from zero gives its negation.

$$3z=-15$$

Divide both sides by 3.

$$z=\frac{-15}{3}$$

Divide -15 by 3 to get -5.

$$z=-5$$