Solve 4/k+1+5/k=3/k

$$\frac { 4 } { k + 1 } + \frac { 5 } { k } = \frac { 3 } { k }$$

Solve for k

$$k=-\frac{1}{3}\approx -0.333333333$$

Steps for Solving Linear Equation

Variable k cannot be equal to any of the values -1,0 since division by zero is not defined. Multiply both sides of the equation by k\left(k+1\right), the least common multiple of k+1,k.

$$k\times 4+\left(k+1\right)\times 5=\left(k+1\right)\times 3$$

Use the distributive property to multiply k+1 by 5.

$$k\times 4+5k+5=\left(k+1\right)\times 3$$

Combine k\times 4 and 5k to get 9k.

$$9k+5=\left(k+1\right)\times 3$$

Use the distributive property to multiply k+1 by 3.

$$9k+5=3k+3$$

Subtract 3k from both sides.

$$9k+5-3k=3$$

Combine 9k and -3k to get 6k.

$$6k+5=3$$

Subtract 5 from both sides.

$$6k=3-5$$

Subtract 5 from 3 to get -2.

$$6k=-2$$

Divide both sides by 6.

$$k=\frac{-2}{6}$$

Reduce the fraction \frac{-2}{6} to lowest terms by extracting and canceling out 2.

$$k=-\frac{1}{3}$$