Question

Simplify the following.

1. x/ (x-(1/2))
2.(x-(1/x))/(x+(1/x))
3.((25/a)-a/5+a)

Answer 1

You should get started with that. What's your plan on the 1st one?

Answer 2

I don't know how to do it...

Answer 3

You are saying you never learned to add fractions by finding a common denominator?
You never learned to divide fractions by the idea of "reciprocal and multiply"?

I do not believe that. You should not be in algebra without having studied and internalized these skills. This is all we are doing. I'll do the first one.

You are faced with this: \(\dfrac{x}{x-\dfrac{1}{2}}\)

Add up the denominator: \(\dfrac{x}{x - \dfrac{1}{2}} = \dfrac{x}{\dfrac{2x}{2} - \dfrac{1}{2}} = \dfrac{x}{\dfrac{2x-1}{2}}\)

Divide with the usual idea, reciprocal and multiply: \(\dfrac{x}{\dfrac{2x-1}{2}} = x\cdot \dfrac{2}{2x-1} = \dfrac{x}{1}\cdot\dfrac{2}{2x-1} = \dfrac{2x}{2x-1}\)

Your turn.

Answer 4

where did you get 2x/2 from?

Answer 5

Common denominator. Multiplied both numerator and denominator by 2, thus creating the desired denominator, without altering the value of the expression. Multiplying by 1 doesn't do anything.

Answer 6

alrighty, i got it thanks.