Answer
(a) True for any value of variable
(b) True only when $x=y$
(c) True only if $y=0$ or $x =1$
(d) True only if $a=0$ and $b$ any value
(e) True for any value of variables
(f) True for any value of variables
Work Step by Step
We will simplify all the equations to check if they are true for all values for variables
(a) This equation is true for any value of variable
$\frac{5+a}{5}=1+\frac{a}{5}$
$\frac{5+a}{5} - \frac{a}{5} = 1$
$\frac{5+a-a}{5} = 1$
$\frac{5}{5} = 1$
$1=1$
(b) This equation is not true for any value for variables, it is true only when $x=y$
$\frac{x+1}{y+1}=\frac{x}{y}$
$\frac{xy+y}{yx+x}=1$
$xy+y=xy+x$
$y=x$
(c) This equation is false for any variables, it's true only if $y=0$ or $x =1$
$\frac{x}{x+y}=\frac{1}{1+y}$
$x+xy=x+y$
$xy-y=0$
$y(x-1)=0$
$y=0; x=1$
(d) True for any value of variables
$2(\frac{a}{b})\ne\frac{2a}{2b}$
$2(\frac{a}{b})\ne(\frac{a}{b})$
(e) True for any value of variables
$\frac{-a}{b}=-\frac{a}{b}$
$-\frac{a}{b}=-\frac{a}{b}$
$1=1$
(f) True for any value of variables.
$\frac{1+x+x^2}{x}=\frac{1}{x}+1+x$
$1+x+x^2=1+x+x^2$
$1=1$
