Is 1/a²- 1/b² divisible by (a-b)???

1.	Is 1/a²- 1/b² divisible by (a-b)???
Answer» align="absmiddle" ALT="\frac{\Big( \frac{1}{a^{2} }- \frac{1}{b^{2}}\Big) }{ (a-b) }" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?F=%20%5Cfrac%7B%5CBig%28%20%5Cfrac%7B1%7D%7Ba%5E%7B2%7D%20%7D-%20%5Cfrac%7B1%7D%7Bb%5E%7B2%7D%7D%5CBig%29%20%7D%7B%20%28a-b%29%20%7D%20" title="\frac{\Big( \frac{1}{a^{2} }- \frac{1}{b^{2}}\Big) }{ (a-b) }"> $= \frac{ \frac{(b^{2} - a^{2})}{a^{2} b^{2} }}{ (a-b) }$ $=\frac{(b+a)(b-a)}{a^{2}b^{2} (a-b)}$ $= \frac{-(b+a)\cancel {(a-b)}}{a^{2}b^{2} \cancel {(a-b)}}$ $= \frac{-(a+b)}{a^{2}b^{2}}$ THEREFORE ., $\red{ \Big( \frac{1}{a^{2}} - \frac{1}{b^{2}}\Big) } \: is \green { \: divisible \: by \: (a-b ) }$ •••♪

Answer»

align="absmiddle" ALT="\frac{\Big( \frac{1}{a^{2} }- \frac{1}{b^{2}}\Big) }{ (a-b) }" class="latex-formula" id="TexFormula1" src="https://tex.z-dn.net/?F=%20%5Cfrac%7B%5CBig%28%20%5Cfrac%7B1%7D%7Ba%5E%7B2%7D%20%7D-%20%5Cfrac%7B1%7D%7Bb%5E%7B2%7D%7D%5CBig%29%20%7D%7B%20%28a-b%29%20%7D%20" title="\frac{\Big( \frac{1}{a^{2} }- \frac{1}{b^{2}}\Big) }{ (a-b) }">

$= \frac{ \frac{(b^{2} - a^{2})}{a^{2} b^{2} }}{ (a-b) }$