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Simplify . (1/c + 1/h)/(1/(c ^ 2) - 1/(r ^ 2))

Simplify 1c 1h1c 2 1r 2 class=

Sagot :

Answer:

[tex]\frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}[/tex]

Step-by-step explanation:

[tex]\frac{\frac{1}{c}+\frac{1}{h}}{\frac{1}{c^2}-\frac{1}{r^2}}[/tex]

Combine [tex]\frac{1}{c} + \frac{1}{h}[/tex]

[tex]\frac{\frac{h+c}{ch}}{\frac{1}{c^2}-\frac{1}{r^2}}[/tex]

Combine the bottom, too.

[tex]=\frac{\frac{h+c}{ch}}{\frac{r^2-c^2}{c^2r^2}}[/tex]

Apply the fraction rule

[tex]=\frac{\left(h+c\right)c^2r^2}{ch\left(r^2-c^2\right)}[/tex]

Cancel

[tex]=\frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}[/tex]

Therefore, [tex]\frac{\left(\frac{1}{c}+\frac{1}{h}\right)}{\left(\frac{1}{\left(c^2\right)}-\frac{1}{\left(r^2\right)}\right)}:\quad \frac{\left(h+c\right)cr^2}{h\left(r^2-c^2\right)}[/tex]

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