Solve 4/2u-3+10/4u^2-9=1/2u+3

$$\frac{ 4 }{ 2u-3 } + \frac{ 10 }{ 4 { u }^{ 2 } -9 } = \frac{ 1 }{ 2u+3 }$$

Solve for u

$$u = -\frac{25}{6} = -4\frac{1}{6} \approx -4.166666667$$

Steps for Solving Linear Equation

Variable u cannot be equal to any of the values -\frac{3}{2},\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2u-3\right)\left(2u+3\right), the least common multiple of 2u-3,4u^{2}-9,2u+3.

$$\left(2u+3\right)\times 4+10=2u-3$$

Use the distributive property to multiply 2u+3 by 4.

$$8u+12+10=2u-3$$

Add 12 and 10 to get 22.

$$8u+22=2u-3$$

Subtract 2u from both sides.

$$8u+22-2u=-3$$

Combine 8u and -2u to get 6u.

$$6u+22=-3$$

Subtract 22 from both sides.

$$6u=-3-22$$

Subtract 22 from -3 to get -25.

$$6u=-25$$

Divide both sides by 6.

$$u=\frac{-25}{6}$$

Fraction \frac{-25}{6} can be rewritten as -\frac{25}{6} by extracting the negative sign.

$$u=-\frac{25}{6}$$