Simplify the expression.?

Question

x^2 -16 * x + 4
_________ _______
x^2 - 49 x - 7

Answer 1

It's hard to read the question, but I presume you mean

[(x^2 - 16) / (x^2 - 49)] divided by [(x + 4) / (x - 7)]

The first step is to factor. Note that in both cases, we have a difference of squares, and a difference of squares a^2 - b^2 is factored out like (a - b) (a + b). We factor the exact same way.

[ {(x - 4) (x + 4)} / {(x - 7) (x + 7)} ] divided by [(x + 4) / (x - 7) ]

Recall that when we divide fractions, we multiply by the reciprocal.

[ {(x - 4) (x + 4)} / {(x - 7) (x + 7)} ] divided by [(x - 7) / (x + 4) ]

Now, remember that fractions can not only be canceled vertically, but diagonally as well; that is, we can cancel terms common to the numerator of the first to the denominator of the second, or the denominator of the first to the numerator of the second, and so forth. The (x + 4) cancels diagonally, for instance, and so does the (x - 7) terms. This leaves us with

(x - 4) / (x + 7)

Answer 2

Please rewrite this without the lines, and the correct operations.