x^2 + 7x divided by x^2 - 49?

Hi,

For this question, you should notice that in the numerator, a common factor of x is present and can be taken out to get:

x[x+7]

Now, in the denominator, we have the difference of squares which allows us to look at the number 49 and realize that it's a perfect square of 7 x 7. However, when factoring, we have to have the opposite signs in the groupings as shown below to prevent a linear term from appearing when using FOIL.

Therefore, we get the following:

x^2 - 49 = (x-7)(x+7)

Therefore, overall, we have:

[x(x+7)] / [(x-7)(x+7)]

Now notice that x+7 is common in both the numerator and denominator and can be cancelled out to get:

x / [x - 7] <=== FINAL ANSWER

I hope that helps you out! Please let me know if you have any other questions!

= (x² + 7x)/(x² - 49)
= (x[x + 7])/([x + 7][x - 7})
= x/(x - 7)

Answer: x/(x - 7)

x (x + 7)
----------------
(x - 7)(x + 7)

x
---------
x - 7

(x^2 + 7x)/(x^2 - 49)
= x(x + 7)/(x^2 + 7x - 7x - 49)
= x(x + 7)/[(x^2 + 7x) - (7x + 49)]
= x(x + 7)/[x(x + 7) - 7(x + 7)]
= x(x + 7)/(x + 7)(x - 7) (cancel out x + 7)
= x/(x - 7)

(x^2 + 7x) /(x^2 - 49)
= x(x + 7)(x + 7)(x – 7)
= x/(x – 7)
you are right
---------

The top of the fraction simplifies to: x(x+7)
The bottom simplifies to: (x+7)(x-7)

The (x+7)'s cancel out, to give the answer of x/(x-7)

yes you are right

x(x+7)/(x+7)(x-7)=x/(x-7)