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docker41 [41]
2 years ago
7

Use the information below to complete the problem: p(x) = (1)/(x + 1)

Mathematics
1 answer:
bija089 [108]2 years ago
8 0

Given:

The functions are:

p(x)=\dfrac{1}{x+1}

q(x)=\dfrac{1}{x-1}

To find:

The rational expression for p(x)-q(x).

Solution:

We have,

p(x)=\dfrac{1}{x+1}

q(x)=\dfrac{1}{x-1}

Now,

p(x)-q(x)=\dfrac{1}{x+1}-\dfrac{1}{x-1}

p(x)-q(x)=\dfrac{(x-1)-(x+1)}{(x+1)(x-1)}

p(x)-q(x)=\dfrac{x-1-x-1}{x^2-1^2}             [\because a^2-b^2=(a-b)(a+b)]

p(x)-q(x)=\dfrac{-2}{x^2-1}

Therefore, the required rational expression for p(x)-q(x) is \dfrac{-2}{x^2-1}.

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