Simplify 3x/(x2-y2) − x/(y-x)

Question

ScanSolve AI Tutor · Accepted Answer

Step 1: Factor the denominator of the first term using the difference of squares formula, a² − b² = (a−b)(a+b). x² − y² = (x−y)(x+y) Step 2: Rewrite the denominator of the second term to match a factor in the first term's denominator. y − x = −(x − y) Step 3: Substitute these factored forms back into the original expression. (3x)/((x−y)(x+y)) − (x)/(−(x−y)) Step 4: Simplify the sign in the second term. (3x)/((x−y)(x+y)) + (x)/(x−y) Step 5: Find a common denominator, which is (x−y)(x+y). Multiply the second term by (x+y)/(x+y). (3x)/((x−y)(x+y)) + (x(x+y))/((x−y)(x+y)) Step 6: Combine the numerators over the common denominator. (3x + x(x+y))/((x−y)(x+y)) Step 7: Distribute x in the numerator and simplify. (3x + x² + xy)/((x−y)(x+y)) Step 8: Factor out x from the numerator. (x(3 + x + y))/((x−y)(x+y)) The simplified expression is: (x(x+y+3))/((x−y)(x+y))

Simplify 3x/(x2-y2) - x/(y-x)

Answer

Step-by-step solution

Factor the denominator of the first term using the difference of squares formula, $a^2 - b^2 = (a-b)(a+b)$ .

Rewrite the denominator of the second term to match a factor in the first term's denominator.

Substitute these factored forms back into the original expression.

Simplify the sign in the second term.

Find a common denominator, which is $(x-y)(x+y)$ .

Combine the numerators over the common denominator.

Distribute $x$ in the numerator and simplify.

Factor out $x$ from the numerator.

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