Simplify the expression state any excluded values 2a^2-4a+2 --------------- 3a^2-3

Question

asked Mar 1, 2020 15.5k views

2 Answers

Claudiu Iordache · Answer 1 · 2020-03-05T07:58:21+0000

Answer:

The simplified form is
.

is the excluded value for the given expression.

Explanation:

Given:

The expression given is:

(2a^2-4a+2)/(3a^2-3)

Let us simplify the numerator and denominator separately.

The numerator is given as
2a^2-4a+2

2 is a common factor in all the three terms. So, we factor it out. This gives,

=2(a^2-2a+1)

Now,
a^2-2a+1=(a-1)(a-1)

Therefore, the numerator becomes
2(a-1)(a-1)

The denominator is given as:
3a^2-3

Factoring out 3, we get

3(a^2-1)

Now,
a^2-1 is of the form
a^2-b^2=(a-b)(a+b)

So,
a^2-1=(a-1)(a+1)

Therefore, the denominator becomes
3(a-1)(a+1)

Now, the given expression is simplified to:

(2a^2-4a+2)/(3a^2-3)=(2(x-1)(x-1))/(3(x-1)(x+1))

There is
(x-1) in the numerator and denominator. We can cancel them only if
$x\\e1$ as for
, the given expression is undefined.

Now, cancelling the like terms considering
$x\\e1$ , we get:

(2a^2-4a+2)/(3a^2-3)=(2(x-1))/(3(x+1))

Therefore, the simplified form is

The simplification is true only if
$x\\e1$ . So,
is the excluded value for the given expression.