Solve Algebra Word Problem: x+1/x - 1/4 = x+3/x+2

[homegrown898]

http://www26.brinkster.com/nick898/question.htm

I`ve scanned the question so you can understand it better. This is how
I started...

x+1/x - 1/4 = x+3/x+2

But this is how far I got. I don`t know what do after this part and I
don`t even know if what I`m doing is correct.

 

[Pseudo Statistic]

I'll show what I got..
The original one should be (x+1)/x
And it's saying that (x+3)/(x+2) = (x+1)/x - 1/4
So you aren't far off... not you can use your favourite method of solving rational expressions.. my way of choice is cross-multiply...
In the end, x = -4 || 2
Then go on from there..

 

[thepatientmental]

Can anyone help me?

To solve this algebra word problem, we first need to find a common denominator for all the fractions involved. In this case, the common denominator is 4x(x+2). We can rewrite the equation as:

4x(x+2)(x+1)/4x(x+2) - (x+2)/4x(x+2) = 4x(x+2)(x+3)/4x(x+2) + (x+1)/4x(x+2)

Now, we can combine the fractions on the left side and the fractions on the right side:

(4x^2 + 8x + 4 - x - 2)/4x(x+2) = (4x^2 + 12x + 6 + x + 1)/4x(x+2)

Simplifying further, we get:

(4x^2 + 7x + 2)/4x(x+2) = (4x^2 + 13x + 7)/4x(x+2)

Now, we can subtract both sides by (4x^2 + 13x + 7)/4x(x+2):

(4x^2 + 7x + 2)/4x(x+2) - (4x^2 + 13x + 7)/4x(x+2) = 0

Simplifying, we get:

-6x/4x(x+2) = 0

Dividing both sides by -6/4x(x+2), we get:

x = 0

Therefore, the solution to this algebra word problem is x = 0. You can plug in this value for x in the original equation to check if it satisfies the equation. I hope this helps!