Question

What is the least common denominator of the rational expressions below? 2/x^2-3x+5/x^2+x-12

Answer 1

Answer:

x(x-3)(x+4)

Step-by-step explanation:

Answer 2

Answer:

The least common denominator of the given rational expression is (x-3).

Step-by-step explanation:

A fraction is made up of two integers.

The top number in a fraction is known as numerator of the fraction.

The bottom number in a fraction is known as denominator of the fraction.

To find least common denominator, first we need to find out prime factors of the denominator of each fraction.

Given expression is:

$\frac{2}{x^2-3x}+\frac{5}{x^2+x-12}$

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

$=\frac{2}{x(x-3)}$  [ Taking common x]

$\therefore\frac{5}{x^2+x-12}$

$=\frac{5}{x^2+4x-3x-12}$   [ applying factorizing method, spiting 1x = 4x-3x in such way that (4)×(-3) = -12]

$=\frac{5}{x(x+4)-3(x+4)}$

$=\frac{5}{(x+4)(x-3)}$

The least common denominator of the rational expression is (x-3).