Question

Subtract 3/x−1 – 4/x+3 . A. −x+13(x−1)(x+3) ; x ≠ –3 or 1 B. −x+5(x−1)(x+3) ; x ≠ –3 or 1 C. 7x+5(x−1)(x+3) ; x ≠ –3 or 1 D. 7x+13(x−1)(x+3) ; x ≠ –3 or 1

Answer 1

Answer: (-x + 13)/(x - 1)(x + 3); x ≠ -3 or 1.

Explanation:

3/(x - 1) - 4/(x + 3) = 3(x + 3)/[(x - 1)(x + 3)] - 4(x - 1)/[(x - 1)(x + 3)]

Simplifying the expression, we get:

3(x + 3)/[(x - 1)(x + 3)] - 4(x - 1)/[(x - 1)(x + 3)] = [3(x + 3) - 4(x - 1)]/[(x - 1)(x + 3)]

= [3x + 9 - 4x + 4]/[(x - 1)(x + 3)] = (-x + 13)/[(x - 1)(x + 3)]

Therefore, the answer is A. (-x + 13)/(x - 1)(x + 3); x ≠ -3 or 1.

Answer 2

Answer: To subtract fractions, we need a common denominator. The least common multiple of x-1 and x+3 is (x-1)(x+3), so we'll use that as our common denominator. Then we have:

3/(x-1) - 4/(x+3) = (3(x+3))/(x-1)(x+3) - (4(x-1))/(x-1)(x+3)

Simplifying the numerators, we get:

= (3x + 9 - 4x + 4)/(x-1)(x+3)

= (-x + 13)/(x-1)(x+3)

Therefore, the answer is A. -x+13(x−1)(x+3) for x ≠ –3 or 1.

Explanation: