## FlyinSolo_424 3 years ago Simplify

1. FlyinSolo_424

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2. nphuongsun93

$\huge \frac{1}{81} - \frac{1}{x^2}$factor this using a^2-b^2 = (a+b)(a-b)

3. mayank_mak

use $a ^{2} - b ^{2} = (a-b)\times (a+b)$

4. FlyinSolo_424

5. Wired

$\Large \frac{1}{Z}*\frac{1}{Z} = \frac{1}{Z^{2}}$ $81 = Z^{2}$

6. mayank_mak

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7. FlyinSolo_424

Ok Someone is going to have to go step by step Im confused.

8. Wired

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

9. Wired

$\LARGE \frac{\frac{1}{9}-\frac{1}{x}}{(\frac{1}{9}+\frac{1}{x})(\frac{1}{9}-\frac{1}{x})} = \frac{1}{(\frac{1}{9}+\frac{1}{x})}$

10. UnkleRhaukus

$\Large\frac{\frac{1}{9}-\frac1x}{\frac 1{81}-\frac 1{x^2}}$ multiply the nuemerator and denominator of the big fraction by $$81x^2$$ $\Large=\frac{81x^2\left(\frac{1}{9}-\frac1x\right)}{81x^2\left(\frac 1{81}-\frac 1{x^2}\right)}$distribute $\Large=\frac{\left(\frac{81x^2}{9}-\frac{81x^2}x\right)}{\left(\frac {81x^2}{81}-\frac {81x^2}{x^2}\right)}$simplify$\large=\frac{{9x^2}-81x}{x^2-81}$ factorise$=\frac{9x(x-9)}{(x+9)(x-9)}$cancel$=\frac{9x\cancel{(x-9)}}{(x+9)\cancel{(x-9)}}$$\large=\frac{9x}{x+9}$