SOLUTION: Can someone explain to me the steps so i can understand them.thanks ... Problem #1 Write in simplest form. (5)/(12) + (1)/(4) Problem #2 Multiply. (3x-27)/(x^2+5x

Question 74326: Can someone explain to me the steps so i can understand them.thanks ...
Problem #1
Write in simplest form.
(5)/(12) + (1)/(4)

Problem #2
Multiply.
(3x-27)/(x^2+5x) * (2x)/(9-x) this symbol "*" means multiply.

Problem # 3
Divide
(x^2-4y^2)/(8x^2-16y) divided by ((x^2+2xy))

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Can someone explain to me the steps so i can understand them.thanks ...
Problem #1
Write in simplest form.
(5)/(12) + (1)/(4)
You can only add fractions if they have the same denominator.
The "least common denominator" for your problem is 12.
Rewrite each fraction with 12 as its denominator, as follows:
5/12 + 3/12
Now you can add the fractions:
=8/12
Now you can reduce the fraction:
=2/3
---------------

Problem #2
Multiply.
(3x-27)/(x^2+5x) * (2x)/(9-x) this symbol "*" means multiply.
To multiply fractions it sometimes helps to first factor the pieces:
=(3(x-9)) / (x(x+5) * 2x / -(x-9)
Since (x-9) is in the numerator and in the denominator, cancel it:
3/(x(x+5) * 2x / (-1)
Since "x" is in the numerator and in the denominator, cancel it.
3/(x+5) *2/(-1)
Multiply numerators then multiply denominators to get:
= -6/(x+5)
--------------------
Problem # 3
Divide
(x^2-4y^2)/(8x^2-16y) divided by ((x^2+2xy))
To divide you have to invert the denominator and multiply:
[(x-2y)(x+2y)/[8(x^2-2y)]/[x(x+2y)]
Cancel the (x+2y) factor to get:
(x-2y)/[8(x^2-2y)]/x
=(x-2y)/8x(x^2-2y)
------------
Cheers,
Stan H.

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