Question

determine the restriction of
3x
2x-4​

Answer 1

Answer:

Let's first find the restrictions:

This can be done by factoring the denominator of the expression.

3x−2x+3+7(x−4)(x+3)

A restriction in a rational expression occurs when the denominator equals 0, since division by 0 in mathematics is undefined.

Therefore, we must now set the factors in the denominator to 0 and solve for x. These will be our restrictions.

x+3=0andx−4=0

x=−3andx=4

Therefore, x≠−3,4

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Now, let's simplify:

This can be done by placing everything on a common denominator.

Since both expressions already has (x+3) as a factor in the denominator, and only one has (x−4), we must multiply the expression to the left by (x−4) to make it equivalent to the one on the right.

(3x−2)(x−4)(x+3)(x−4)+7(x+3)(x−4)

=3x2−14x+8+7(x+3)(x−4)

=3x2−14x+15(x+3)(x−4)

The trinomial in the numerator is factorable. Always factor it when possible to see if anything can be simplified. You will be docked marks if you don't simplify fully. I factored this one and nothing needs to be eliminated. This is in simplest form.

Hopefully this helps!