Difference of squares: Equations with denominators

Question 1

Resolve:

$\frac{x^2-9}{x-3}=0$

Question 2

Does the following equation have a true or false value?

$\frac{x^2-81}{(x-9)(x+9)}=1$

Question 3

Resolve:

$\frac{x^2+4}{3}=3(x-2)(x+2)$

Question 4

Resolve:

$\frac{-7}{x+4}=x-4$

Examples with solutions for Difference of squares: Equations with denominators

Resolve:

$\frac{x^2-9}{x-3}=0$

Does the following equation have a true or false value?

$\frac{x^2-81}{(x-9)(x+9)}=1$

True only when $x\ne\pm9$ .

Resolve:

$\frac{x^2+4}{3}=3(x-2)(x+2)$

$\operatorname{\pm}\sqrt{5}$

Resolve:

$\frac{-7}{x+4}=x-4$

$\pm3$