Solve 1/5x+6-2/x-1=0

$$\frac { 1 } { 5 x + 6 } - \frac { 2 } { x - 1 } = 0$$

Solve for x

$$x = -\frac{13}{9} = -1\frac{4}{9} \approx -1.444444444$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{6}{5},1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(5x+6\right), the least common multiple of 5x+6,x-1.

$$x-1-\left(5x+6\right)\times 2=0$$

Use the distributive property to multiply 5x+6 by 2.

$$x-1-\left(10x+12\right)=0$$

To find the opposite of 10x+12, find the opposite of each term.

$$x-1-10x-12=0$$

Combine x and -10x to get -9x.

$$-9x-1-12=0$$

Subtract 12 from -1 to get -13.

$$-9x-13=0$$

Add 13 to both sides. Anything plus zero gives itself.

$$-9x=13$$

Divide both sides by -9.

$$x=\frac{13}{-9}$$

Fraction \frac{13}{-9} can be rewritten as -\frac{13}{9} by extracting the negative sign.

$$x=-\frac{13}{9}$$