Question

write the rational expressions as equivalent rational expressions with the lowest common denominator

Answer 1

1. The equivalent rational expression with the lowest common denominator of   $\frac{2}{3d^{2} + 14d^{2} - 5 }$   is $\frac{2}{(d+5)(3d-1)}$

2. The equivalent rational expression with the lowest common denominator of $\frac{3d}{3d^{2} - 22d + 7}$  is $\frac{3d}{(d-7)(3d-1)}$

1.

  $\frac{2}{3d^{2} + 14d^{2} - 5 }$

Let factorise the denominator below

3d² + 14d - 5

-15 and 14

Two numbers we can multiply to get -15 and add to get 14 are 15 and -1.

Therefore,

3d²- d + 15d - 5

d(3d - 1) + 5(3d - 1)

(d+5)(3d-1)

Therefore, the equivalent rational expression with the lowest common denominator will be

$\frac{2}{(d+5)(3d-1)}$

2.

$\frac{3d}{3d^{2} - 22d + 7}$

Factorise the denominator

3d²- 22d+7

3d²- d - 21d + 7

d(3d - 1) - 7(3d - 1)

(d - 7)(3d - 1)

Therefore, the equivalent rational expression with the lowest common denominator will be

$\frac{3d}{(d-7)(3d-1)}$

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