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timurjin [86]
3 years ago
13

Simplify the expression given below. x+2/4x^2+5x+1 * 4x+1/x^2-4

Mathematics
1 answer:
GenaCL600 [577]3 years ago
8 0

Answer:

\frac{1}{(x+1)(x-2)}

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)}

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Step-by-step explanation:

From the midpoint theorem, which states that the line that a line drawn such that it joins the midpoints of two sides of a triangle, is parallel to the third side of the triangle and is equal to half the length of the third side

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