Precalculus Examples

$F = G \frac{m M}{r^{2}}$

Step 1

Rewrite the equation as $G (\frac{m M}{r^{2}}) = F$ .

$G (\frac{m M}{r^{2}}) = F$

Step 2

Combine $G$ and $\frac{m M}{r^{2}}$ .

$\frac{G m M}{r^{2}} = F$

Step 3

Multiply both sides by $r^{2}$ .

$\frac{G m M}{r^{2}} r^{2} = F r^{2}$

Step 4

Simplify the left side.

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Step 4.1

Cancel the common factor of $r^{2}$ .

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Step 4.1.1

Cancel the common factor.

$\frac{G m M}{r^{2}} r^{2} = F r^{2}$

Step 4.1.2

Rewrite the expression.

$G m M = F r^{2}$

Step 5

Divide each term in $G m M = F r^{2}$ by $G M$ and simplify.

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Step 5.1

Divide each term in $G m M = F r^{2}$ by $G M$ .

$\frac{G m M}{G M} = \frac{F r^{2}}{G M}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $G$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{G m M}{G M} = \frac{F r^{2}}{G M}$

Step 5.2.1.2

Rewrite the expression.

$\frac{m M}{M} = \frac{F r^{2}}{G M}$

Step 5.2.2

Cancel the common factor of $M$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{m M}{M} = \frac{F r^{2}}{G M}$

Step 5.2.2.2

Divide $m$ by $1$ .

$m = \frac{F r^{2}}{G M}$