Question

What is the simplified form of (x+1)/(x^2+x-6) ÷ (x^2+5x+4)/(x+4) ? 1) 1/(x+3)(x+4) 2) 1/(x+3)(x-2) 3) 1/(x+4)(x-2) 4) 1/(x+3)(x+1)

Answer 1

To simplify the given expression, multiply the numerator by the reciprocal of the denominator and cancel out common factors. The simplified form of the expression is 1/(x+3)(x+4).

Step-by-step explanation:

To simplify the expression (x+1)/(x^2+x-6) ÷ (x^2+5x+4)/(x+4), we can start by multiplying the numerator by the reciprocal of the denominator. This gives us (x+1)/(x+4) * (x+4)/(x^2+x-6). Next, we can cancel out common factors between the numerator and denominator. The (x+4) terms cancel out, leaving us with (x+1)/(x^2+x-6). The simplified form of the expression is therefore 1/(x^2+x-6), which corresponds to option 1) 1/(x+3)(x+4).

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