Solve for x (x+9)/(x-5)=(x-7)/(x+7)

Problem

(x+9)/(x−5)=(x−7)/(x+7)

Solution

1. Cross-multiply the fractions to eliminate the denominators.

(x+9)*(x+7)=(x−7)*(x−5)

2. Expand both sides of the equation using the FOIL method.

x^2+7*x+9*x+63=x^2−5*x−7*x+35

3. Combine like terms on each side.

x^2+16*x+63=x^2−12*x+35

4. Subtract x^2 from both sides to simplify the equation.

16*x+63=−12*x+35

5. Isolate the variable by adding 12*x to both sides and subtracting 63 from both sides.

28*x=−28

6. Divide by 28 to solve for x

x=−1

Final Answer

(x+9)/(x−5)=(x−7)/(x+7)⇒x=−1

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