Solve x+1/x-3=x+3/x-5

$$\frac{ x+1 }{ x-3 } = \frac{ x+3 }{ x-5 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 3,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x-3\right), the least common multiple of x-3,x-5.

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

Use the distributive property to multiply x-5 by x+1 and combine like terms.

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

Consider \left(x-3\right)\left(x+3\right). Multiplication can be transformed into difference of squares using the rule: \left(a-b\right)\left(a+b\right)=a^{2}-b^{2}. Square 3.

$$x^{2}-4x-5=x^{2}-9$$

Subtract x^{2} from both sides.

$$x^{2}-4x-5-x^{2}=-9$$

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

$$-4x-5=-9$$

Add 5 to both sides.

$$-4x=-9+5$$

Add -9 and 5 to get -4.

$$-4x=-4$$

Divide both sides by -4.

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

Divide -4 by -4 to get 1.

$$x=1$$