Solve 5x-8/x^2-9-1=3-x/x+3

$$\frac{ 5x-8 }{ { x }^{ 2 } -9 } -1= \frac{ 3-x }{ x+3 }$$

Solve for x

$$x=10$$

Steps for Solving Linear Equation

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

$$5x-8+\left(x-3\right)\left(x+3\right)\left(-1\right)=\left(x-3\right)\left(3-x\right)$$

Use the distributive property to multiply x-3 by x+3 and combine like terms.

$$5x-8+\left(x^{2}-9\right)\left(-1\right)=\left(x-3\right)\left(3-x\right)$$

Use the distributive property to multiply x^{2}-9 by -1.

$$5x-8-x^{2}+9=\left(x-3\right)\left(3-x\right)$$

Add -8 and 9 to get 1.

$$5x+1-x^{2}=\left(x-3\right)\left(3-x\right)$$

Use the distributive property to multiply x-3 by 3-x and combine like terms.

$$5x+1-x^{2}=6x-x^{2}-9$$

Subtract 6x from both sides.

$$5x+1-x^{2}-6x=-x^{2}-9$$

Combine 5x and -6x to get -x.

$$-x+1-x^{2}=-x^{2}-9$$

Add x^{2} to both sides.

$$-x+1-x^{2}+x^{2}=-9$$

Combine -x^{2} and x^{2} to get 0.

$$-x+1=-9$$

Subtract 1 from both sides.

$$-x=-9-1$$

Subtract 1 from -9 to get -10.

$$-x=-10$$

Multiply both sides by -1.

$$x=10$$