Solve x-4/x+3=x-3/x+1

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

Solve for x

$$x = \frac{5}{3} = 1\frac{2}{3} \approx 1.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -3,-1 since division by zero is not defined. Multiply both sides of the equation by \left(x+1\right)\left(x+3\right), the least common multiple of x+3,x+1.

$$\left(x+1\right)\left(x-4\right)=\left(x+3\right)\left(x-3\right)$$

Use the distributive property to multiply x+1 by x-4 and combine like terms.

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

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.

$$x^{2}-3x-4=x^{2}-9$$

Subtract x^{2} from both sides.

$$x^{2}-3x-4-x^{2}=-9$$

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

$$-3x-4=-9$$

Add 4 to both sides.

$$-3x=-9+4$$

Add -9 and 4 to get -5.

$$-3x=-5$$

Divide both sides by -3.

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

Fraction \frac{-5}{-3} can be simplified to \frac{5}{3} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{5}{3}$$