Divide. Show all work. Make sure to simplify. Assume no denominator equals zero x^2-144/x^2+7x-60 divided by 3x-36/9x-45
I'm really confused on this and if anyone can help, I'd appreciate it. Thanks!
x^2-144 = (x-12)(x+12)
x^2+7x-60 = (x+12)(x-5)
3x-36 = 3(x-12)
9x-45 = 9(x-5)
So, since dividing by a fraction is the same as multiplying by its reciprocal, we really have
(x-12)(x+12) / (x-5)(x+12) * 9(x-5) / 3(x-12)
Now you can see that almost everything cancels out, leaving you with just a value of
3
There's an (x-12) top and bottom, (x+12) top and bottom, and (x-5) top and bottom.
Thank you! That makes so much more sense now!
To divide the given expression, first factorize the numerator and the denominator.
Numerator (x^2 - 144) can be written as (x - 12)(x + 12).
Denominator (x^2 + 7x - 60) can be factored as (x + 12)(x - 5).
So the expression can be written as ((x - 12)(x + 12)) / ((x + 12)(x - 5)).
Now, let's factorize the other denominator as well.
Denominator (3x - 36) can be factored as 3(x - 12).
So the expression becomes ((x - 12)(x + 12)) / ((x + 12)(x - 5)) divided by (3(x - 12)) / (9x - 45).
Now comes the simplification part. For division, we can multiply by the reciprocal of the second fraction. The reciprocal of (3(x - 12)) / (9x - 45) is (9x - 45) / (3(x - 12)).
So, the expression becomes:
((x - 12)(x + 12)) / ((x + 12)(x - 5)) * ((9x - 45) / (3(x - 12))).
Now, cancel out the common factors:
((x - 12) * 1) / ((x + 12) * (x - 5)) * ((9x - 45) / (3 * 1)).
Simplifying further:
(x - 12) / ((x + 12) * (x - 5)) * (3x - 15).
Final answer:
(x - 12)(3x - 15) / (x + 12)(x - 5).
Remember to always check for any restrictions or values that make the denominator equal to zero. In this case, x cannot be equal to -12 or 5.