Simplify: 5a/6bc² + 3b/8a²c?

Question

How do you handle the Lowest Common Denominator (LCD)? Specifically, what do you do to the numerators after you've found the LCD?

This is the specific problem I am inquiring about:

5a/6bc² + 3b/8a²c

I need to know what to do to the numerator after I find the lowest common denominator.

Here's the step I'm confused about:

(multiply a²/a² and bc/bc)

20a^3 + 9b²c
-----------------------------
24a²bc² + 24a²bc²

How do you arrive at the "a^3" and "b²c" in the numerators?

Answer 1

5a 3b
------ + ---------=
6b^2 8a^2c


5a*8a^2c + 6bc^2*b
--------------------------= (you add the rational numbers)
8a^2c*6bc^2



40a^3c + 18b^2c^2
------------------------= (you multiply the expressions)
48a^2bc^3



2c(20a^3+9b^2c)
---------------------= (you factorize using the LCD=2)
48a^2bc^3



the simplest form:

20a^3+9b^2c
-----------------
24a^2bc^2

Answer 2

Let's use an LCD of 24a²bc²

So the numerator of the first fraction gets multiplied by 4a²
The numerator of the second fraction gets multiplied by 3bc

(20a^3 + 9b²c) / 24a²bc²

Final answer.

You can see that MustBet and Johnny both arrive at the same answer as I do. That is the correct answer.

I will try to explain how we get the two numerators.

If you multiply the top and bottom of the first fraction by 4a², you get

20a^3 / 24a²bc²

If you multiply the top and bottom of the second fraction by 3bc, you get

9b²c / 24a²bc²

and by magic, the denominators of the two fractions are now the same. Thus we can add them:

(20a^3 + 9b²c) / 24a²bc²

Answer 3

Take these two fractions:

1/12 + 1/3

The LCD is 12, so you have to multiply 1/12 by 1/1 and 1/3 by 4/4 to get fractions that you can add together.

Just do the same with your fractions.

Answer 4

first multiply and divide by abc
5a/6bc² + 3b/8a²c
1/abc[5a*abc/6bc²+3b*abc/8a²c]
now you get a simplified form without getting confused
1/abc[5a²/6c+3b²/8a]
we can even simplify
1/2abc[5a²/3c+3b²/4a]
now the denominator is simplied and not similar in anyway. you cannot get an lcd
so
1/2abc[5a² * 4a+3b² * 3c/4a*3c]
1/2abc[20a^3+9b² c/12ac]
this is the answer i feel instead of this 5a/6bc² + 3b/8a²c it is this way 5a/6b² c+ 3b/8a²c

Answer 5

common denominator 24. a^2. b .c^2

divide this by first denominator.
Multiply the first fraction by quotient

do the same for the second fraction.

Answer 6

5a + 3b
---------------------------
6bc² + 8a²c


need common denominators to add: (multiply 4/4 and 3/3)

20a + 9b
----------------------------
24bc² + 24a²c


(multiply a²/a² and bc/bc)

20a^3 + 9b²c
-----------------------------
24a²bc² + 24a²bc²


answer:

20a^3 + 9b²c
----------------
24a²bc²

This is as in simplest form...