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54. If

f(x)=\frac{x}{x^{2}-16}

and

g(x)=\frac{7}{x^{2}+5 x+4}

, find $f(x)-g(...

Jan 22, 2024

54. If

f(x)=\frac{x}{x^{2}-16}

and

g(x)=\frac{7}{x^{2}+5 x+4}

, find

f(x)-g(x)

. a.

\frac{x^{2}-6 x+28}{(x-4)(x+4)}

\frac{x^{2}-6}{(x-4)(x+4)}

\frac{x^{2}-6 x+28}{(x-4)(x+4)(x+1)}

\frac{x^{2}+6 x+28}{(x-4)(x+4)(x+1)}

\frac{x^{2}-6 x-28}{\left(x^{2}-16\right)(x+1)}

Generated Graph

Solution by Steps

step 2

Factor the denominators of both fractions. The first denominator factors to

(x - 4)(x + 4)

and the second factors to

(x + 1)(x + 4)

step 3

To subtract the fractions, we need a common denominator, which is

(x - 4)(x + 4)(x + 1)

step 4

Rewrite both fractions with the common denominator and simplify the numerator

step 5

The simplified form of

f(x) - g(x)

\frac{x^2 - 6x + 28}{(x - 4)(x + 4)(x + 1)}

according to the asksia-ll calculation

Key Concept

Simplifying Rational Expressions

Explanation

To simplify the difference of two rational expressions, factor the denominators, find a common denominator, and combine the numerators accordingly.