Solve 4x=a/x-8+3/x+5

$$4x = \frac{ a }{ x-8 } + \frac{ 3 }{ x+5 }$$

Solve for a

$$a=-\frac{\left(x-8\right)\left(3-20x-4x^{2}\right)}{x+5}$$

$$x\neq 8\text{ and }x\neq -5$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-8\right)\left(x+5\right), the least common multiple of x-8,x+5.

$$4x\left(x-8\right)\left(x+5\right)=\left(x+5\right)a+\left(x-8\right)\times 3$$

Use the distributive property to multiply 4x by x-8.

$$\left(4x^{2}-32x\right)\left(x+5\right)=\left(x+5\right)a+\left(x-8\right)\times 3$$

Use the distributive property to multiply 4x^{2}-32x by x+5 and combine like terms.

$$4x^{3}-12x^{2}-160x=\left(x+5\right)a+\left(x-8\right)\times 3$$

Use the distributive property to multiply x+5 by a.

$$4x^{3}-12x^{2}-160x=xa+5a+\left(x-8\right)\times 3$$

Use the distributive property to multiply x-8 by 3.

$$4x^{3}-12x^{2}-160x=xa+5a+3x-24$$

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

$$xa+5a+3x-24=4x^{3}-12x^{2}-160x$$

Subtract 3x from both sides.

$$xa+5a-24=4x^{3}-12x^{2}-160x-3x$$

Combine -160x and -3x to get -163x.

$$xa+5a-24=4x^{3}-12x^{2}-163x$$

Add 24 to both sides.

$$xa+5a=4x^{3}-12x^{2}-163x+24$$

Combine all terms containing a.

$$\left(x+5\right)a=4x^{3}-12x^{2}-163x+24$$

Divide both sides by x+5.

$$\frac{\left(x+5\right)a}{x+5}=\frac{\left(x-8\right)\left(4x^{2}+20x-3\right)}{x+5}$$

Dividing by x+5 undoes the multiplication by x+5.

$$a=\frac{\left(x-8\right)\left(4x^{2}+20x-3\right)}{x+5}$$