simplify

[blndchic0822]

The problem is:

1/x - 1/5
__________

1/x[sup:3vmianlf]2[/sup:3vmianlf] - 1/25



I've tried cross multiplying to find common denominators and then cancelling out; however it never results in the correct answer show on the answer sheet which is...

5x / x+5

 

[mmm4444bot]

I've tried cross multiplying to find common denominators I'm not sure what this means.

How about a different approach.

Factor the denominator as a difference of squares.

 

[blndchic0822]

i multiplied 1 times 5 and x times 1 on top to get 5-x, then did the same on the bottom to get 25 - x[sup:3b4q32j3]2[/sup:3b4q32j3].
i took a negative out of (5-x) to have -(x-5) on top and did the same on the bottom to have -(x[sup:3b4q32j3]2[/sup:3b4q32j3]-25).
i factored the bottom into -(x+5)(x-5), which leads to cancelling out the (x-5) on the top and bottom...
leaving me with...

-1
_____
-(x+5)

which is not the correct answer.

 

[mmm4444bot]

i multiplied 1 times 5 and x times 1 on top to get 5-x This is okay, on the top, but you didn't finish the top. The common denominator is 5x.

The top is now:

(5 - x)/(5x)

then did the same on the bottom to get 25 - x[sup:2z3lo8lg]2[/sup:2z3lo8lg] Again, that's not the entire bottom; you left off the common denominator.

The bottom is now:

(25 - x^2)/(25x^2)

Are you familiar with the following relationship?

(a/b)/(c/d) = (a/b)*(d/c)

 

[Mrspi]

The problem is:

1/x - 1/5
__________

1/x[sup:2pmp7l4v]2[/sup:2pmp7l4v] - 1/25



I've tried cross multiplying to find common denominators and then cancelling out; however it never results in the correct answer show on the answer sheet which is...

5x / x+5

You've got a complex fraction here. One way to change a complex fraction to a simple fraction is to multiply the numerator and the denominator of the complex fraction by the Least Common Denominator of all of the fractions within the complex fraction.

In your problem, the least common denominator for 1/x, 1/5, 1/x[sup:2pmp7l4v]2[/sup:2pmp7l4v] and 1/25 is 25 x[sup:2pmp7l4v]2[/sup:2pmp7l4v]

Multiply numerator and denominator of the complex fraction by 25x[sup:2pmp7l4v]2[/sup:2pmp7l4v]:

25x[sup:2pmp7l4v]2[/sup:2pmp7l4v] * (1/x - 1/5)
-----------------------------------
25x[sup:2pmp7l4v]2[/sup:2pmp7l4v]* (1/x[sup:2pmp7l4v]2[/sup:2pmp7l4v] - 1/25)

25x - 5x[sup:2pmp7l4v]2[/sup:2pmp7l4v]
------------------------
25 - x[sup:2pmp7l4v]2[/sup:2pmp7l4v]

Now...factor the numerator and the denominator:

5x(5 - x)
----------------
(5 - x)(5 + x)

Reduce the fraction.....