The question is a fraction that needs to be worked out, that's why I said over:) Please help me for my test and I'll rank you the highest I promise!?
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This problem involves factoring trinomials and simplifying rationals. The numerator is a special product that you need to recognize through practice and memorization.
x^2 - 49
both x^2, and 49 are perfect squares, this product is called a difference of perfect squares because they are being subtracted.
The formula looks like this.
a^2 - b^2 = (a + b)(a - b)
You can expand x^2 - 49 to a general form trinomial by making the "b" term = 0.
x^2 - 49 = x^2 + 0x -49
this factors to (x + 7)(x - 7) and if you foil it you will see that the middle terms will cancel. Now to your problem.
(x^2 - 49) / (x + 7)
{(x + 7)(x - 7)} / (x + 7)... difference of perfect squares
(x - 7)...the (x + 7) factors reduced to 1
x - 7
x^2 - 49
both x^2, and 49 are perfect squares, this product is called a difference of perfect squares because they are being subtracted.
The formula looks like this.
a^2 - b^2 = (a + b)(a - b)
You can expand x^2 - 49 to a general form trinomial by making the "b" term = 0.
x^2 - 49 = x^2 + 0x -49
this factors to (x + 7)(x - 7) and if you foil it you will see that the middle terms will cancel. Now to your problem.
(x^2 - 49) / (x + 7)
{(x + 7)(x - 7)} / (x + 7)... difference of perfect squares
(x - 7)...the (x + 7) factors reduced to 1
x - 7
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(x^2 - 49)/(x + 7) =
(x + 7)(x - 7)/(x + 7) =
x - 7
(x + 7)(x - 7)/(x + 7) =
x - 7
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(x^2-49)/(x+7)
(x-7)(x+7)/(x+7)
(x-7)/1
(x-7)(x+7)/(x+7)
(x-7)/1
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x^2-49 (x-7)(x+7)
_____ = ________ = x-7 [x+7]:[x+7]=1
x + 7 x+7
_____ = ________ = x-7 [x+7]:[x+7]=1
x + 7 x+7
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(x^2-49) = (x+7)(x-7)
(x+7)(x-7)
-------------- =
x+7
x-7
(x+7)(x-7)
-------------- =
x+7
x-7