Simplify the expression given below. x+2/4x^2+5x+1 * 4x+1/x^2-4
1 answer:
Answer:
Step-by-step explanation:
![\frac{x+2}{4x^2 + 5x + 1} \ \times \ \frac{4x+1}{x^2-4}\\\\=\frac{x+2}{4x^2 + 4x + x + 1} \ \times \ \frac{4x+1}{x^2-2^2}\\\\=\frac{x+2}{4x(x + 1) + 1( x + 1)} \ \times \ \frac{4x+1}{(x - 2)(x + 2)} \ \ \ \ \ \ \ \ [ \ (a^2 - b^2 = (a-b)(a+b) \ ]\\\\\\=\frac{x+2}{(4x + 1)(x+1)} \ \times \ \frac{4x+1}{(x-2)(x+2)}\\\\=\frac{1}{(x+1)} \ \times \ \frac{1}{(x-2)}\\\\= \frac{1}{(x+1)(x-2)}](https://tex.z-dn.net/?f=%5Cfrac%7Bx%2B2%7D%7B4x%5E2%20%2B%205x%20%2B%201%7D%20%5C%20%5Ctimes%20%5C%20%5Cfrac%7B4x%2B1%7D%7Bx%5E2-4%7D%5C%5C%5C%5C%3D%5Cfrac%7Bx%2B2%7D%7B4x%5E2%20%2B%204x%20%20%2B%20x%20%2B%201%7D%20%5C%20%5Ctimes%20%5C%20%5Cfrac%7B4x%2B1%7D%7Bx%5E2-2%5E2%7D%5C%5C%5C%5C%3D%5Cfrac%7Bx%2B2%7D%7B4x%28x%20%2B%201%29%20%20%2B%201%28%20x%20%2B%201%29%7D%20%5C%20%5Ctimes%20%5C%20%5Cfrac%7B4x%2B1%7D%7B%28x%20-%202%29%28x%20%2B%202%29%7D%20%20%20%20%5C%20%5C%20%5C%20%5C%20%5C%20%20%5C%20%5C%20%5C%20%5B%20%5C%20%28a%5E2%20-%20b%5E2%20%3D%20%28a-b%29%28a%2Bb%29%20%5C%20%5D%5C%5C%5C%5C%5C%5C%3D%5Cfrac%7Bx%2B2%7D%7B%284x%20%2B%201%29%28x%2B1%29%7D%20%5C%20%5Ctimes%20%5C%20%5Cfrac%7B4x%2B1%7D%7B%28x-2%29%28x%2B2%29%7D%5C%5C%5C%5C%3D%5Cfrac%7B1%7D%7B%28x%2B1%29%7D%20%5C%20%5Ctimes%20%5C%20%5Cfrac%7B1%7D%7B%28x-2%29%7D%5C%5C%5C%5C%3D%20%5Cfrac%7B1%7D%7B%28x%2B1%29%28x-2%29%7D)
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