Can one of you mighty fine people tell me how to go from the left to the right side?

Can one of you mighty fine people tell me how to go from the left to the right side?
I'm trying to get into maths in my free time, but I don't know how to do this... can someone show me the way?

It's a "1" btw, now an "I"

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codecogs.com/latex/eqneditor.php
khanacademy.org/math/algebra/polynomial-factorization/factoring-quadratics-1/v/factoring-simple-quadratic-expression
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(1/3)+(4/2)=(4*3)+(1*2)/(2*3)=14/6

You just have to put b+1 inside the fraction
Not trying to be rude user, but this is middle school tier

How old are you? I never made it past algebra 2 in high school, started college late at 22 years old not remembering shit, and now I'm studying real analysis. There's still hope for you, if you care enough. The really neat and interesting stuff starts coming after calc 2, you just have to hang in there long enough.

There are multiple ways to verify that

1. Multiply out both sides to get two quadratic polynomials in b and then compare their coefficients to see if they're equal.

2. See if you can convert one expression to the other by factoring common terms and applying other similar tricks.

3. Check if the equality holds for any 3 distinct values of b. Two different quadratics can agree at no more than 2 values, so if the two sides are equal at 3 values, that means they're equal at all values.

add b+1 on top and expand the equation
get (b^2 + 3b + 2)/2
factorise the numerator to get RHS

Thanks for your help guys!

You weren't rude, no worries.

b(b + 1)/2 + b + 1
=(b + 1)*b/2 + (b + 1)*1
=(b + 1)(b/2 + 1)
=(b+1)(b+2)/2

[math]\frac{b(b+1)}{2}+b+1=\frac{b(b+1)}{2}+\frac{2(b+1)}{2}=\frac{b(b+1)+2(b+1)}{2}=\frac{b^2+b+2b+2}{2}=\frac{(b+2)(b+1)}{2}=\frac{(b+1)(b+2)}{2}[/math]

Goddamn, I meant:
[math]\frac{b(b+1)}{2}+b+1=\frac{b(b+1)}{2}+\frac{2(b+1)}{2}=\frac{b(b+1)+2(b+1)}{2}=\frac{(b+2)(b+1)}{2}=\frac{(b+1)(b+2)}{2}[/math]