Solve 63/8+x=63/3-x

$$\frac { 63 } { 8 + x } = \frac { 63 } { 3 - x }$$

Solve for x

$$x = -\frac{5}{2} = -2\frac{1}{2} = -2.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -8,3 since division by zero is not defined. Multiply both sides of the equation by \left(x-3\right)\left(x+8\right), the least common multiple of 8+x,3-x.

$$\left(x-3\right)\times 63=-\left(8+x\right)\times 63$$

Use the distributive property to multiply x-3 by 63.

$$63x-189=-\left(8+x\right)\times 63$$

Multiply -1 and 63 to get -63.

$$63x-189=-63\left(8+x\right)$$

Use the distributive property to multiply -63 by 8+x.

$$63x-189=-504-63x$$

Add 63x to both sides.

$$63x-189+63x=-504$$

Combine 63x and 63x to get 126x.

$$126x-189=-504$$

Add 189 to both sides.

$$126x=-504+189$$

Add -504 and 189 to get -315.

$$126x=-315$$

Divide both sides by 126.

$$x=\frac{-315}{126}$$

Reduce the fraction \frac{-315}{126} to lowest terms by extracting and canceling out 63.

$$x=-\frac{5}{2}$$