Solve x+4/x-5=x+3/x-2

$$\frac { x + 4 } { x - 5 } = \frac { x + 3 } { x - 2 }$$

Solve for x

$$x = -\frac{7}{4} = -1\frac{3}{4} = -1.75$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 2,5 since division by zero is not defined. Multiply both sides of the equation by \left(x-5\right)\left(x-2\right), the least common multiple of x-5,x-2.

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

Use the distributive property to multiply x-2 by x+4 and combine like terms.

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

Use the distributive property to multiply x-5 by x+3 and combine like terms.

$$x^{2}+2x-8=x^{2}-2x-15$$

Subtract x^{2} from both sides.

$$x^{2}+2x-8-x^{2}=-2x-15$$

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

$$2x-8=-2x-15$$

Add 2x to both sides.

$$2x-8+2x=-15$$

Combine 2x and 2x to get 4x.

$$4x-8=-15$$

Add 8 to both sides.

$$4x=-15+8$$

Add -15 and 8 to get -7.

$$4x=-7$$

Divide both sides by 4.

$$x=\frac{-7}{4}$$

Fraction \frac{-7}{4} can be rewritten as -\frac{7}{4} by extracting the negative sign.

$$x=-\frac{7}{4}$$