Solve by Factoring 6/(x+5)=1-1/(x-5)

Subtract ${\displaystyle 1}$ from both sides of the equation.

Add ${\displaystyle \frac{1}{x-5}}$ to both sides of the equation.

To write ${\displaystyle -1}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{x+5}{x+5}}$.

Combine ${\displaystyle -1}$ and ${\displaystyle \frac{x+5}{x+5}}$.

Combine the numerators over the common denominator.

Simplify the numerator.

To write ${\displaystyle \frac{-x+1}{x+5}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{x-5}{x-5}}$.

To write ${\displaystyle \frac{1}{x-5}}$ as a fraction with a common denominator, multiply by ${\displaystyle \frac{x+5}{x+5}}$.

Write each expression with a common denominator of ${\displaystyle (x+5)(x-5)}$, by multiplying each by an appropriate factor of ${\displaystyle 1}$.

Combine the numerators over the common denominator.

Simplify the numerator.

Factor ${\displaystyle -1}$ out of ${\displaystyle -x}$.

Rewrite ${\displaystyle 7}$ as ${\displaystyle -1(-7)}$.

Factor ${\displaystyle -1}$ out of ${\displaystyle -\left(x\right)-1(-7)}$.

Rewrite ${\displaystyle -(x-7)}$ as ${\displaystyle -1(x-7)}$.

Move the negative in front of the fraction.

If any individual factor on the left side of the equation is equal to ${\displaystyle 0}$, the entire expression will be equal to ${\displaystyle 0}$.

Set ${\displaystyle x}$ equal to ${\displaystyle 0}$.

Set ${\displaystyle x-7}$ equal to ${\displaystyle 0}$ and solve for ${\displaystyle x}$.

The final solution is all the values that make ${\displaystyle x(x-7)=0}$ true.