Show that (3x+2)/(x+1)=3-((1)/(x+1))?

Method 1 :

L.H.S.
= (3x + 2) / (x + 1)
= [(3x + 3) - 1] / (x + 1)
= [3(x + 1) - 1] / (x + 1)
= [3(x + 1) / (x + 1)] - [1 / (x + 1)]
= 3 - [1 / (x + 1)]
= R.H.S.

Hence, (3x + 2) / (x + 1) = 3 - [1 / (x + 1)]


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Method 2 :

R.H.S.
= 3 - [1 / (x + 1)]
= [3(x + 1) / (x + 1)] - [1 / (x + 1)]
= [3(x + 1) - 1] / (x + 1)
= (3x + 3 - 1) / (x + 1)
= (3x + 2) / (x + 1)
= L.H.S.

Hence, (3x + 2) / (x + 1) = 3 - [1 / (x + 1)]

that's a hard one

I think to do this, it's easier to start with the right side and make it look like the left side.

You want to show that:

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

So let's start with that right side:

3 - 1 / (x + 1)

To subtract fractions, we need a common denominator, so:

3(x + 1) / (x + 1) - 1 / (x + 1)

Now we can subtract the numerators:

[3(x + 1) - 1] / (x + 1)

Simplify the numerator:

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

And now it looks like the left side. So I've shown that they are equal.