simplify rational exprssion: [1/(m-1) + 2/(m+2)]/[2/(m+2) - 1/(m-3)]

[sean1]

Hello everyone,
I am hoping someone can help me with this problem. So far is I was told to follow these three steps:
1. Find the least common denominator for all fractions
2. Multiply the numerator & denominator by the LCD
3. simplify
I think I am lost on the first step, which is finding the Least Common Denominator (LCD). I am pretty sure the LCD is (m-1)(m+2)(m-3). Is this correct? If so, could someone please show me how to apply the next two steps to get the answer? Thank you so much

Simplify the following:

. . . . .\(\displaystyle \dfrac{\left(\dfrac{1}{m\, -\, 1}\, +\, \dfrac{2}{m\, +\, 2}\right)}{\left(\dfrac{2}{m\, +\, 2}\, -\, \dfrac{1}{m\, -\, 3}\right)}\)

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fractions:

   1       2
 ----- + -----
 m - 1   m + 2
===============
   2       1
 ----- - -----
 m + 2   m - 3

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[Denis]

So far is I was told to follow these three steps:
1. Find the least common denominator for all fractions
2. Multiply the numerator & denominator by the LCD
3. simplify
I think I am lost on the first step, which is finding the Least Common Denominator (LCD).
I am pretty sure the LCD is (m-1)(m+2)(m-3). Is this correct?
If so, could someone please show me how to apply the next two steps to get the answer?
Simplify:

1 + 2
m-1 m+2
--------------
2 - 1
m+2 m-3

Yikes! Try this:

u = m-1
v = m+2
w = m-3

(1/u + 2/v) / (2/v - 1/w)

Simplify that, then substitute back in...

 

[Dr.Peterson]

Hello everyone,
I am hoping someone can help me with this problem. So far is I was told to follow these three steps:
1. Find the least common denominator for all fractions
2. Multiply the numerator & denominator by the LCD
3. simplify
I think I am lost on the first step, which is finding the Least Common Denominator (LCD). I am pretty sure the LCD is (m-1)(m+2)(m-3). Is this correct? If so, could someone please show me how to apply the next two steps to get the answer? Thank you so much

Simplify:

1 + 2
m-1 m+2
--------------
2 - 1
m+2 m-3

The standard way to do this is to multiply each term in the numerator, and each term in the denominator, by the LCD which you have correctly identified. In each term a factor of the LCD will cancel with the denominator, leaving you with just a product for each term. That is, it will no longer be a "complex fraction". Then you can "just" simplify as usual -- that is, expand each product, combine like terms, and see if there is a common factor between numerator and denominator.

Let us see your answer, and your work if it isn't too much, and we can tell you whether you did it all correctly.