Solve 5/x^2-7x+12+-2/x-3=-5/x-4

$$\frac { 5 } { x ^ { 2 } - 7 x + 12 } + \frac { - 2 } { x - 3 } = \frac { - 5 } { x - 4 }$$

Solve for x

$$x=\frac{2}{3}\approx 0.666666667$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 3,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x-3\right), the least common multiple of x^{2}-7x+12,x-3,x-4.

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

Use the distributive property to multiply x-4 by -2.

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

Add 5 and 8 to get 13.

$$13-2x=\left(x-3\right)\left(-5\right)$$

Use the distributive property to multiply x-3 by -5.

$$13-2x=-5x+15$$

Add 5x to both sides.

$$13-2x+5x=15$$

Combine -2x and 5x to get 3x.

$$13+3x=15$$

Subtract 13 from both sides.

$$3x=15-13$$

Subtract 13 from 15 to get 2.

$$3x=2$$

Divide both sides by 3.

$$x=\frac{2}{3}$$