Math help?? Multiplying and Dividing Rational Expressions?

Question

Could someone help me with these problems?? Thanks so much

1. 4 times (x plus 2) over 5 x times 6x squared over 2xx

2. 25 minus x squared over 12 times 6 over 5 minus x

3. a squared minus 9 over a squared all muliplied by a squared minus 3 a over a squared plus a minus 12

Answer 1

It's easier if you use normal notation, so that it's easier to follow. I'm guessing on a couple of these.

1.) (4(x + 2) / 5x) * (6x^2 / 2x)

Step 1: Combine fractions by multiplying the nominator first, then the denominator.

(4(x + 2) / 5x) * (6x^2 / 2x) = (4(x + 2) * 6x^2) / (5x * 2x)
24x^2(x + 2) / 10x^2

Step 2: Simplify by cancelling out common factors between the nominator and denominator.
24 / 10 = 12 / 5
the x^2's cancel, leaving:
12(x+2) / 5

2.) ((25 - x^2) / 12) * (6 / (5 - x)

Step 1: Factor out 25 - x^2, using difference of two squares.
x^2 - a^2 = (x + a)(x - a)
25 - x^2 = (5 + x)(5 - x)

Step 2: Combine fractions by multiplying the nominator first, then the denominator.
((5 + x)(5 - x)/ 12) * (6 / (5 - x) = (6(5 + x)(5 - x)) / (12(5 - x))

Step 3: Simplify by cancelling out common factors between the nominator and denominator.
(5 - x) cancels
6/12 = 1/2, leaving:
(5 + x) / 2

3.) (a^2 - 9 / a^2) * ((a^2 - 3a) / (a^2 + a - 12))

Step 1: Factor each binomial.
a^2 - 9 = a^2 - 3^2 = (a + 3)(a - 3)
a^2 - 3a = a(a - 3)
a^2 + a - 12 = (a + 4)(a - 3)

Step 2: Combine fractions by multiplying the nominator first, then the denominator.
((a + 3)(a - 3) / a^2) * (a(a - 3) / (a + 4)(a - 3)) = (a(a + 3)(a - 3)^2) / (a^2(a + 4)(a - 3)

Step 3: Simplify by cancelling out common factors between the nominator and denominator.
one of the (a - 3) cancels
a/a^2 = 1/a, leaving:
(a + 3)(a - 3) / (a(a + 4)) or (a^2 - 9) / (a^2 + 4a)

Answer 2

and in case you ask your self how the guy above me have been given (2w +3)(w-5) from 2w^2 - 7w - 15: first write out (2w + _)(x - _) now u choose the factors of -15 which may be the two +3 and -5 or -3 and +5 additionally think approximately that the coefficient (as a result that is 2) whilst thinking for the factors of the final extensive style. in this question, the (2w + 3) became probable portion of the simplification of the 2w^2 - 7w - 15 so as that makes issues plenty much less confusing.