Solve 2/u-5=-3/2u-10+2

$$\frac { 2 } { u - 5 } = - \frac { 3 } { 2 u - 10 } + 2$$

Solve for u

$$u = \frac{27}{4} = 6\frac{3}{4} = 6.75$$

Steps for Solving Linear Equation

Variable u cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by 2\left(u-5\right), the least common multiple of u-5,2u-10.

$$2\times 2=-3+2\left(u-5\right)\times 2$$

Multiply 2 and 2 to get 4.

$$4=-3+2\left(u-5\right)\times 2$$

Multiply 2 and 2 to get 4.

$$4=-3+4\left(u-5\right)$$

Use the distributive property to multiply 4 by u-5.

$$4=-3+4u-20$$

Subtract 20 from -3 to get -23.

$$4=-23+4u$$

Swap sides so that all variable terms are on the left hand side.

$$-23+4u=4$$

Add 23 to both sides.

$$4u=4+23$$

Add 4 and 23 to get 27.

$$4u=27$$

Divide both sides by 4.

$$u=\frac{27}{4}$$