Solve 10/x-2-3x+1/x^2-4=3/x+2

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

Solve for x

$$x = -\frac{25}{4} = -6\frac{1}{4} = -6.25$$

Steps for Solving Linear Equation

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

$$\left(x+2\right)\times 10-\left(3x+1\right)=\left(x-2\right)\times 3$$

Use the distributive property to multiply x+2 by 10.

$$10x+20-\left(3x+1\right)=\left(x-2\right)\times 3$$

To find the opposite of 3x+1, find the opposite of each term.

$$10x+20-3x-1=\left(x-2\right)\times 3$$

Combine 10x and -3x to get 7x.

$$7x+20-1=\left(x-2\right)\times 3$$

Subtract 1 from 20 to get 19.

$$7x+19=\left(x-2\right)\times 3$$

Use the distributive property to multiply x-2 by 3.

$$7x+19=3x-6$$

Subtract 3x from both sides.

$$7x+19-3x=-6$$

Combine 7x and -3x to get 4x.

$$4x+19=-6$$

Subtract 19 from both sides.

$$4x=-6-19$$

Subtract 19 from -6 to get -25.

$$4x=-25$$

Divide both sides by 4.

$$x=\frac{-25}{4}$$

Fraction \frac{-25}{4} can be rewritten as -\frac{25}{4} by extracting the negative sign.

$$x=-\frac{25}{4}$$