I with a Complex Rational Expression

[Charlie123]

Homework Statement

Homework Equations

Idk what to do after I multiply the LCD I get confused please help me.

The Attempt at a Solution

All I know is that the LCD is (x+5)(x+1)(x-2) and when I multiply into every fraction I get this.
(X+5)(X-2)(X-2) - (X+5)(X+1)(X+1)
-------------------------------------
(X+5)(X+1)(X+1) - (X+5)(X-2)(X-2)

 

[praharmitra]

you are right... continue... is anything canceling?

are you allowed to cancel similar algebraic equations?? what condition must you put to cancel the common term in the denominator and numerator

 

[Charlie123]

you are right... continue... is anything canceling?

are you allowed to cancel similar algebraic equations?? what condition must you put to cancel the common term in the denominator and numerator

I don't know where to go from there do I subtract like terms like (x+5) since there's a minus sign inbetween them. And yeah we can cancel similar algebraic equations like top and bottom that are the same we strike them out and replace them with 1's.

 

[epenguin]

Instead of slogging through detailed calculations you should notice that it has all been made up out of only two expressions (quadratics). Call them a and b, write your expression just in terms of a and b and hopefully the answer will jump off the page!

 

[Charlie123]

(x+5)(x-2) - (x+5)(x+1)
---------- ----------
(x+5)(x+1) (x+5)(x-2)
--------------------------
(x+5)(x+1) - (x+5)(x-2)
----------- -----------
(x+5)(x-2) (x+5)(x+1)

So I factor them than I multiply times the LCD which (x+5)(x+1)(x-2)

I got this.

(x+5)(x-2)(x-2) - (x+5)(x+1)(x+1)
-----------------------------------
(x+5)(x+1)(x+1) - (x+5)(x-2)(x-2)

Than I subtracted like terms (x+5) which left me with this.

(x-2)(x-2)(x+1)(x+1)
---------------------
(x+1)(x+1)(x-2)(x-2)

I cancel like terms which is everything so I got this

1
--- = 1
1

What do you guys think does that look right?

 

[epenguin]

Something like, but not quite.
The more complicated a calculation the more the chances of mistake. So why do an unnecessarily complicated one?

 

[Charlie123]

My college teacher said it had to be done his way in order for us to get the credit. And that's the way he did it but idk it doesn't look right to me.

 

[epenguin]

I have heard that before and then when they saw it the teachers came round and credited extra.

I think it is a positive, a virtue and advantage, to be able to recognise what is special in an expression or problem, and if the point instead is to be able to do the general problem then teachers should give a question that can only be dealt with in the general way.

However if you think you cannot afford to present it any other way, at least do the calculation the easy way first, because then you will be able to recognise your mistake when you did it the hard way and get that right too!