Question

3

Select all the correct answers.
Which factors compose the least common denominator for this difference?
115
32 + 48 - 12
2:2
45
(x - 6)
(x - 2)
2:
(3 - 4)
(3 + 2)
(5 + 6)

Answer 1

2nd, 3rd and 6th

Explanation:

Factorise the denominators of both fractions

x² + 4x - 12 = (x + 6)(x - 2)

2x² - 4x = 2x(x - 2)

The least common denominator is then

2x(x - 2)(x + 6)

Answer 2

The factors that compose the LCF of the difference are :

2x
`\huge\checkmark`

(x - 2)
`\huge\checkmark`

(x + 6)
`\huge\checkmark`

Explanation:

x² + 4x - 12 = x² - 2x + 2x + 4x - 12

= x² - 2x + (6x - 12)

= x(x - 2) + 6(x - 2)

= (x - 2)(x + 6)

2x² - 4x = 2x(x - 2)

We get

2x² - 4x = 2x(x - 2)

x² + 4x - 12 = (x - 2)(x + 6)

then

The least common denominator is 2x(x - 2)(x + 6)