Asked by j
What is the difference?
StartFraction x Over x squared minus 2 x minus 15 EndFraction minus StartFraction 4 Over x squared + 2 x minus 35 EndFraction
StartFraction x squared + 3 x + 12 Over (x minus 3) (x minus 5) (x + 7) EndFraction
StartFraction x (x + 3 minus 12) Over (x + 3) (x minus 5) (x + 7) EndFraction
StartFraction x squared + 3 x + 12 Over (x + 3) (x minus 5) (x + 7) EndFraction
StartFraction x squared + 3 x minus 12 Over (x + 3) (x minus 5) (x + 7) EndFraction
All Answers 1
Answered by
GPT-5 mini
AI
Compute a common denominator. Factor the denominators:
x^2 − 2x − 15 = (x − 5)(x + 3),
x^2 + 2x − 35 = (x − 5)(x + 7).
Common denominator = (x − 5)(x + 3)(x + 7). Convert each fraction:
x/(x^2 − 2x − 15) = x(x + 7)/[(x − 5)(x + 3)(x + 7)] = (x^2 + 7x)/den,
4/(x^2 + 2x − 35) = 4(x + 3)/den = (4x + 12)/den.
Subtract numerators:
(x^2 + 7x) − (4x + 12) = x^2 + 3x − 12.
So the difference is
(x^2 + 3x − 12)/[(x − 5)(x + 3)(x + 7)], with x ≠ 5, −3, −7.
x^2 − 2x − 15 = (x − 5)(x + 3),
x^2 + 2x − 35 = (x − 5)(x + 7).
Common denominator = (x − 5)(x + 3)(x + 7). Convert each fraction:
x/(x^2 − 2x − 15) = x(x + 7)/[(x − 5)(x + 3)(x + 7)] = (x^2 + 7x)/den,
4/(x^2 + 2x − 35) = 4(x + 3)/den = (4x + 12)/den.
Subtract numerators:
(x^2 + 7x) − (4x + 12) = x^2 + 3x − 12.
So the difference is
(x^2 + 3x − 12)/[(x − 5)(x + 3)(x + 7)], with x ≠ 5, −3, −7.
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