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Oksi-84 [34.3K]
3 years ago
6

(b) 4x+3 2x-1 - 2 = 6x+2 2x-1

Mathematics
1 answer:
irga5000 [103]3 years ago
3 0

Answer:

56

Step-by-step explanation:

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\huge \boxed{\mathbb{QUESTION} \downarrow}

  • Simplify ⇨ 1/x(x+a) + 1/x(x-a)

\large \boxed{\mathbb{ANSWER \: WITH \: EXPLANATION} \downarrow}

\sf\frac { 1 } { x ( x + a ) } + \frac { 1 } { x ( x - a ) } \\

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x+a\right) and x\left(x-a\right) is x\left(x+a\right)\left(x-a\right). Multiply \frac{1}{x\left(x+a\right)} times \frac{x-a}{x-a}. Multiply \frac{1}{x\left(x-a\right)} times \frac{x+a}{x+a}.

\sf\frac{x-a}{x\left(x+a\right)\left(x-a\right)}+\frac{x+a}{x\left(x+a\right)\left(x-a\right)}  \\

Because \frac{x-a}{x\left(x+a\right)\left(x-a\right)} and \frac{x+a}{x\left(x+a\right)\left(x-a\right)} have the same denominator, add them by adding their numerators.

\sf\frac{x-a+x+a}{x\left(x+a\right)\left(x-a\right)}  \\

Combine like terms in x-a+x+a.

\sf\frac{2x}{x\left(x+a\right)\left(x-a\right)}  \\

Cancel out x in both the numerator and denominator.

\sf\frac{2}{\left(x+a\right)\left(x-a\right)}  \\

Expand \left(x+a\right)\left(x-a\right).

\boxed{\boxed{ \bf\frac{2}{x^{2}-a^{2}}}}  \\

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