# Division:

x^2 + 2x - 15over 4x^2 divided by x^2 -25 over 2x-10 Will someone show me the steps to work this problem, I have looked and looked at my book but it still makes no sense to me. Help.

First, change the division to the reciprocal of muliplication. Check this, it depends on my understanding of your problem.

(x^2+2x-15) * (2x-10)/(x^2-25)

Now each of those can be factored, do so. It should reduce very quickly.

multiply by the reciprocal of the second fraction (...basically just flip it over)

originally you have....

x^2 + 2x - 15
_____________

4x^2

_______________

x^2 - 25
_________

2x - 10

Then you'll get

x^2 + 2x - 15 2x - 10
_____________ x _________

4x^2 x^2 - 25

Factor everything and simplify

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Hope this helps!!!

sorry i don't know why it came out so messed up.

Anway...

Try to follow the instructions of either bob or I (they are the same)

## To divide the given expression ((x^2 + 2x - 15)/(4x^2)) / ((x^2 - 25)/(2x - 10)), we need to multiply the first term by the reciprocal of the second term.

Step 1: Write the expression as a multiplication problem by flipping the second fraction:

((x^2 + 2x - 15)/(4x^2)) * ((2x - 10)/(x^2 - 25))

Now, let's factor the expressions in the numerators and denominators:

Numerator 1: x^2 + 2x - 15 = (x + 5)(x - 3)
Denominator 1: 4x^2 = 2x * 2x = 2x(2x)

Numerator 2: 2x - 10 = 2(x - 5)
Denominator 2: x^2 - 25 = (x + 5)(x - 5)

Replacing the factors in the expression, we have:

((x + 5)(x - 3)/(2x(2x))) * (2(x - 5)/((x + 5)(x - 5)))

Step 2: Cancel out any common factors:

(x + 5) cancels out in the numerator and denominator.
(x - 5) cancels out in the numerator and denominator.
2 cancels out in the numerator and denominator.

This leaves us with:

((x - 3)/(2x)) * (1/1) = (x - 3)/(2x)

Therefore, the simplified form of ((x^2 + 2x - 15)/(4x^2)) / ((x^2 - 25)/(2x - 10)) is (x - 3)/(2x).