Check the solution to "Write the following fractions in terms of the..."

Cem Hayes

Answered question

2021-11-05

Write the following fractions in terms of the LCD of the fractions.

\frac{x}{x^{2} + x - 6},

and

\frac{6 x}{x^{2} - 9}

sovienesY

Skilled2021-11-06Added 89 answers

Step 1
Given fractions

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

= \frac{x}{(x^{2} + 2 x - 3 x - 6)}

= \frac{x}{x (x + 2) - 3 (x + 2)} = \frac{x}{(x - 3) (x + 2)}

L . C . D . = \frac{x}{(x - 3) (x + 2)}

Step 2

(a^{2} - b^{2} = (a + b) (a - b))

\Rightarrow \frac{6 x}{x^{2} - 9}

\Rightarrow \frac{6 x}{x^{2} - {(3)}^{2}} \Rightarrow \frac{6 x}{(x - 3) (x + 3)}

∴ L . C . D = \frac{6 x}{(x - 3) (x + 3)}

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