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(e) (x-3)/(x+3)=(x-2)/(x+2)

(e) x−3x+3=x−2x+2 \frac{x-3}{x+3}=\frac{x-2}{x+2}

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Full solution

Q. (e) x−3x+3=x−2x+2 \frac{x-3}{x+3}=\frac{x-2}{x+2}
  1. Cross-multiply fractions: Step 11: Cross-multiply to eliminate the fractions.\newline(x−3)(x+2)=(x−2)(x+3)(x - 3)(x + 2) = (x - 2)(x + 3)
  2. Expand and simplify: Step 22: Expand both sides of the equation.x2+2x−3x−6=x2+3x−2x−6x^2 + 2x - 3x - 6 = x^2 + 3x - 2x - 6
  3. Combine like terms: Step 33: Simplify by combining like terms. x2−x−6=x2+x−6x^2 - x - 6 = x^2 + x - 6
  4. Subtract and simplify: Step 44: Subtract x2x^2 from both sides to simplify further.\newline−x−6=x−6-x - 6 = x - 6
  5. Isolate the variable: Step 55: Add 66 to both sides.\newline−x=x-x = x
  6. Add and solve: Step 66: Add xx to both sides to isolate the variable.\newline0=2x0 = 2x
  7. Final solution: Step 77: Divide both sides by 22 to solve for xx.x=0x = 0

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