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# (3x+9/2x-6)•(4x+4/x+3)

write a simplified expression for the area of the rectangle. State all restrictions on x

### 3 Answers by Expert Tutors

Bill F. | Experienced Teacher & Tutor in Round Rock, TXExperienced Teacher & Tutor in Round Roc...
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I read your question as  [(3x+9) / (2x-6)] * [(4x+4) / (x+3)].  Assuming that's correct:

Multiply both numerators and both denominators:

(12x2 + 12x  +36x + 36) / (2x2 + 6x - 6x - 18)

= (12x2 + 48x + 36) / (2x2 -18).

Factor:  12(x2 + 4x + 3) / 2(x2 - 9) = 12(x+3)(x+1) / 2(x+3)(x-3)

Divide numerator and denominator by 2(x+3):  6(x+1) / (x-3).

Since a denominator cannot = 0, x cannot = +3, because if x=+3, then (x-3) = (+3-3) = 0

Ame S. | Well-rounded tutor specializing in science and mathematicsWell-rounded tutor specializing in scien...
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I am assuming that the terms are (3x), (9/2x), (-6), (4x), (4/x), and (3).  It was unclear in the notation if this was the case.

Each term in one parenthetical quantity must be multiplied by each term in the other parenthetical quantity.

12x2+12+9x+18+(18/x)+(27/2x)-24-(24/2x)-18

Group the like terms (x2, x, etc.).  At this point, you can change those terms over x to terms over 2x to help group terms.

12x2-15c+(15/2x)+12

All of these numbers are divisible by 3.

3(4x2-5x+[5/2x]+4)

Because dividing by 0 is undefined, anything that will result in a denominator's being 0 is a restriction.

2x is the denominator, so x cannot be 0.

Kevin S. |
5.0 5.0 (4 lesson ratings) (4)
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Brosky:

I'm assuming that the expression is [(3x+9)/(2x-6)] * [(4x+4)/(x+3)]

If so, there are a few steps to take:

1 - Since multiplication (and its inverse operation division) is commutative, we can multiply the numerators and divide by the product of the denominators:

[(3x+9)(4x+4)]/[(2x-6)(x+3)]

2 - Now, see if you can pull factors out of the numerator or denominator to see if it can be reduced:

[(3)(x+3)(4)(x+1)]/[(2)(x-3)(x+3)]

We can reduce the (x+3) from the numerator and denominator, and reduce the (4) and (2), which leaves us with the simplified equation

[(3)(2)(x+1)]/[(x-3)(x+3)] = [6 (x+1)]/ (x-3)(x-3)]

3. For restrictions on x, we need to find any values of x that would make the denominator equal to 0 (zero), which means that either

x - 3 = 0 or

x + 3 = 0

which follows tha ift x = 3 or x = -3,  the denominator = 0. Therefore, the restrictions are (in sentence form), x = all real numbers such that x is not equal to 3 and x is not equal to -3