Solve for x (x-2)/(x+4)=(x-6)/(x-4)

Problem

(x−2)/(x+4)=(x−6)/(x−4)

Solution

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

(x−2)*(x−4)=(x−6)*(x+4)

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

x2−4*x−2*x+8=x2+4*x−6*x−24

3. Simplify the terms on each side by combining like terms.

x2−6*x+8=x2−2*x−24

4. Subtract x2 from both sides to eliminate the quadratic term.

−6*x+8=−2*x−24

5. Isolate the variable x by adding 6*x and 24 to both sides.

8+24=−2*x+6*x

32=4*x

6. Divide by the coefficient of x to find the solution.

x=32/4

x=8

Final Answer

(x−2)/(x+4)=(x−6)/(x−4)⇒x=8

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