how does t^2 / t+1 become t-1 + 1/(t+1)

[nickname]

how does t^2 / t+1 become t-1 + 1/(t+1) ?

i know that a/ b+c = a/b + a/c

but when I follow this formula I get (t^2/t+1) + (1/t+1)

Could anyone tell me what step I am doing wrong?

Thank you for the help!

 

[soroban]

Hello, nickname!

\(\displaystyle \text{How does }\,\frac{t^2}{t+1}\,\text{ become }\,t-1 + \frac{1}{t+1}\) ?

\(\displaystyle \text{i know that: }\;\frac{a}{b+c} \:=\:\frac{a}{b} +\frac{a}{c}\) . . Arrgh! Who told you that?

\(\displaystyle \text{Use long division . . .}\)

. . \(\displaystyle \begin{array}{cccccccc} &&&& t & - & 1 \\ & & -- & -- & -- & -- & -- \\ t+1 & ) & t^2 \\ & & t^2 & + & t \\ & & -- & -- & -- \\ & & & & -t \\ & & & & -t & - & 1 \\ & & & & -- & -- & -- \\ & & & & & & 1 \end{array}\)


\(\displaystyle \text{Therefore: }\;\frac{t^2}{t+1} \;\;=\;\;t-1 + \frac{1}{t+1}\)

 

[nickname]

Thank you! Sorry I wrote wrong formula. a+b/c = a/c + b/c

Thanks again!