Solve 5*6/x-1=9/x+1

$$5 \cdot \frac { 6 } { x - 1 } = \frac { 9 } { x + 1 }$$

Solve for x

$$x = -\frac{13}{7} = -1\frac{6}{7} \approx -1.857142857$$

Steps for Solving Linear Equation

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

$$5\left(x+1\right)\times 6=\left(x-1\right)\times 9$$

Multiply 5 and 6 to get 30.

$$30\left(x+1\right)=\left(x-1\right)\times 9$$

Use the distributive property to multiply 30 by x+1.

$$30x+30=\left(x-1\right)\times 9$$

Use the distributive property to multiply x-1 by 9.

$$30x+30=9x-9$$

Subtract 9x from both sides.

$$30x+30-9x=-9$$

Combine 30x and -9x to get 21x.

$$21x+30=-9$$

Subtract 30 from both sides.

$$21x=-9-30$$

Subtract 30 from -9 to get -39.

$$21x=-39$$

Divide both sides by 21.

$$x=\frac{-39}{21}$$

Reduce the fraction \frac{-39}{21} to lowest terms by extracting and canceling out 3.

$$x=-\frac{13}{7}$$