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omeli [17]
3 years ago
9

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

Mathematics
1 answer:
chubhunter [2.5K]3 years ago
8 0

Answer:

The simplified form is \dfrac{2(x-1)}{3(x+1)}.

x =1 is the excluded value for the given expression.

Step-by-step explanation:

Given:

The expression given is:

\dfrac{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:

\frac{2a^2-4a+2}{3a^2-3}=\frac{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\ne1 as for x=1, the given expression is undefined.

Now, cancelling the like terms considering x\ne1, we get:

\dfrac{2a^2-4a+2}{3a^2-3}=\dfrac{2(x-1)}{3(x+1)}

Therefore, the simplified form is \dfrac{2(x-1)}{3(x+1)}

The simplification is true only if  x\ne1. So, x =1 is the excluded value for the given expression.

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