Question

Which shows the rational expression written using the least common denominator? X-2/x3+x+1/2x

Answer 1

Question:

Which shows the rational expression written using the least common denominator?

$\frac{x-2}{x^3} +\frac{x+1}{2x^3}$

Answer:

$\frac{3(x-1)}{2x^3}$

Solution:

Given expression is

$\frac{x-2}{x^3} +\frac{x+1}{2x^3}$

Denominators of the fraction are $x^3$ and $2x^3$.

Factors of $x^3=x\times x\times x$

Factors of $2x^3=2\times x \times x \times x$

Least common factors = $x\times x\times x \times2=2x^3$

Now make the denominators same using LCM.

$\frac{x-2}{x^3} +\frac{x+1}{2x^3}=\frac{(x-2)\times 2}{x^3 \times 2} +\frac{x+1}{2x^3}$

                      $=\frac{2x-4}{2x^3} +\frac{x+1}{2x^3}$

                      $=\frac{2x-4+x+1}{2x^3}$

                      $=\frac{3x-3}{2x^3}$

                      $=\frac{3(x-1)}{2x^3}$

Hence the answer is $\frac{3(x-1)}{2x^3}$.