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

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

Solve for x

$$x = -\frac{53}{10} = -5\frac{3}{10} = -5.3$$

Steps for Solving Linear Equation

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

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

To find the opposite of 6+x, find the opposite of each term.

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

Use the distributive property to multiply -6-x by 9.

$$-54-9x=x-1$$

Subtract x from both sides.

$$-54-9x-x=-1$$

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

$$-54-10x=-1$$

Add 54 to both sides.

$$-10x=-1+54$$

Add -1 and 54 to get 53.

$$-10x=53$$

Divide both sides by -10.

$$x=\frac{53}{-10}$$

Fraction \frac{53}{-10} can be rewritten as -\frac{53}{10} by extracting the negative sign.

$$x=-\frac{53}{10}$$