Question

What is the simplified form of the rational expression below 5x2-5/3x2+3x

Answer 1

Answer:

(5(x-1))/3x

Step-by-step explanation:

Answer 2

Answer:

$\frac{5(x-1)}{3x}$

Step-by-step explanation:

The given expression is

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

To simplify this rational expression, we need to extract the greatest common factor of each part,

$\frac{5x^{2} -5}{3x^{2}+3x}=\frac{5(x^{2}-1) }{3x(x+1)}$

Then, we observe that the numerator has a difference of two perfect squares, which can be factored as

$a^{2} -b^{2} =(a-b)(a+b)$

Where, $a=x$ and $b=1$

$x^{2} -1=(x-1)(x+1)$

Now, we applied this to the rational expression

$\frac{5x^{2} -5}{3x^{2}+3x}=\frac{5(x^{2}-1) }{3x(x+1)}=\frac{5(x-1)(x+1)}{3x(x+1)}=\frac{5(x-1)}{3x}$

Therefore the simplified form of the given expression is

$\frac{5(x-1)}{3x}$