When you have to divide by a fraction, you first invert the divisor, and then multiply the fractions. I'm sure you know that, and you've done it with numbers a hundred times. But you got scared when you saw the 'x's in this one.
Invert the divisor, and then multiply the fractions. That makes the problem say
1 / (x-10) times ( x² - 9x - 10) / 9x
I'm pretty sure you can handle that.
Do you need me to tell you how to multiply two fractions ?
Oh gee whiz ! I just looked at it some more. The second numerator ... the long one ... is (x-10)(x+1). So the (x-10) can cancel out of the top and bottom, and the product of the two fractions becomes
(x+1) / (9x) .
without even writing anything down.
I didn't want to go all the way and give you the answer. But once the snowball started rolling, it wouldn't stop.
Exact steps are shown in the attached picture. Note that when we are dividing fractions, we convert the division into multiplication and flip the second term (divisor)
