What is the sum of the rational expressions below? 3x/x+9 + x/x-4

Question

asked Feb 11, 2020 64.5k views

2 Answers

Jeckep · Answer 1 · 2020-02-13T14:55:34+0000

Answer:

(4x^2-3x)/((x+9)(x-4))

Explanation:

The sum of two rational expressions is done in the following way:

(a)/(b)+(c)/(d) = (a*d + c*b)/(b*d)

In this case we have the following rational expressions

(3x)/(x+9) + (x)/(x-4)

So:

$a=3x\\d=(x+9)\\c=x\\d=(x-4)$

Therefore

(3x)/(x+9) + (x)/(x-4)=(3x(x-4)+x(x+9))/((x+9)(x-4))

simplifying we obtain:

$(3x(x-4)+x(x+9))/((x+9)(x-4))=(3x^2-12x+x^2+9x)/((x+9)(x-4))\\\\(3x^2-12x+x^2+9x)/((x+9)(x-4))=(4x^2-3x)/((x+9)(x-4))$

Meziantou · Answer 2 · 2020-02-15T16:46:50+0000

Answer:

(4x^2-3x)/((x+9)(x-4))

Explanation:

We are given the following expression and we are to find the sum of this rational expression below:

$\frac { 3 x } { x + 9 } + \frac { x } { x - 4 }$

Taking LCM of it to get:

(3x)/(x+9) =(3x(x-4))/((x+9)(x-4))

(x)/(x-4) =(x(x+9))/((x-4)(x+9))

(3x(x-4))/((x+9)(x-4))+(x(x+9))/((x-4)(x+9))

(3x(x-4)+x(x-9))/((x+9)(x-4))

(4x^2-3x)/((x+9)(x-4))