Question

$is \frac{4x+4}{4} equivalent to \frac{x+4}{4} ?$

is $\frac{2}{a+b} the same as \frac{2}{a} + \frac{2}{b} ?$

is (a+b)$(a+b){2} equivalent to a{2} + b^{2}$

Answer 1

$\dfrac{4x+4}{4}\ \text{not equivelent to}\ \dfrac{x+4}{4}\\\\\dfrac{4x+4}{4}=\dfrac{4(x+1)}{4}=x+1\neq\dfrac{x+4}{4}\\---------------------------------\\\dfrac{2}{a+b}\ \text{not equivelent to}\ \dfrac{2}{a}+\dfrac{2}{b}\\\\\dfrac{2}{a}+\dfrac{2}{b}=\dfrac{2b}{ab}+\dfrac{2a}{ab}=\dfrac{2b+2a}{ab}=\dfrac{2(a+b)}{ab}\neq\dfrac{2}{a+b}\\--------------------------------------\\(a+b)^2 \ \text{not equivelent to}\ a^2+b^2\\\\(a+b)^2=(a+b)(a+b)=a^2+ab+ab+b^2=a^2+2ab+b^2\neq a^2+b^2$