Solve 2k-2/5k+3/5k=k-1/k

$$\frac { 2 k - 2 } { 5 k } + \frac { 3 } { 5 k } = \frac { k - 1 } { k }$$

Solve for k

$$k=2$$

Steps for Solving Linear Equation

Variable k cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by 5k, the least common multiple of 5k,k.

$$2k-2+3=5\left(k-1\right)$$

Add -2 and 3 to get 1.

$$2k+1=5\left(k-1\right)$$

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

$$2k+1=5k-5$$

Subtract 5k from both sides.

$$2k+1-5k=-5$$

Combine 2k and -5k to get -3k.

$$-3k+1=-5$$

Subtract 1 from both sides.

$$-3k=-5-1$$

Subtract 1 from -5 to get -6.

$$-3k=-6$$

Divide both sides by -3.

$$k=\frac{-6}{-3}$$

Divide -6 by -3 to get 2.

$$k=2$$