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Rearrange this equation to isolate c.

a=b (1/c-1/d)

Sagot :

Leora03

Answer:

[tex]c=\frac{bd}{ad+b}[/tex]

Step-by-step explanation:

By isolating the term c, we are trying to arrive at the equation c= ____.

[tex]a=b(\frac{1}{c}-\frac{1}{d} )[/tex]

Divide both sides by b:

[tex]\frac{a}{b}= \frac{1}{c}-\frac{1}{d}[/tex]

Add [tex]\bf{\frac{1}{d}[/tex] to both sides:

[tex]\frac{1}{c} =\frac{a}{b} +\frac{1}{d}[/tex]

Rewriting the right-hand side as a single fraction:

[tex]\frac{1}{c} =\frac{a(d)}{b(d)} +\frac{1(b)}{d(b)}[/tex]

[tex]\frac{1}{c} =\frac{ad+b}{bd}[/tex]

Find the expression of c:

[tex]1\div\frac{1}{c} =1\div\frac{ad+b}{bd}[/tex]

[tex]\bf{c=\frac{bd}{ad+b}[/tex]

Additional:

For a similar question on making a variable the subject of formula, do check out: https://brainly.com/question/11000305

semsee45

Answer:

[tex]c=\dfrac{bd}{ad+b}[/tex]

Step-by-step explanation:

Given equation:

[tex]a=b\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

Divide both sides by b:

[tex]\implies \dfrac{a}{b}=\dfrac{b}{b}\left(\dfrac{1}{c}-\dfrac{1}{d}\right)[/tex]

[tex]\implies \dfrac{a}{b}=\dfrac{1}{c}-\dfrac{1}{d}[/tex]

Add 1/d to both sides:

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}-\dfrac{1}{d}+\dfrac{1}{d}[/tex]

[tex]\implies \dfrac{a}{b}+\dfrac{1}{d}=\dfrac{1}{c}[/tex]

[tex]\textsf{Simplify the left side by applying the fraction rule} \quad \dfrac{p}{q}+\dfrac{r}{s}=\dfrac{ps+qr}{qs}:[/tex]

[tex]\implies \dfrac{ad+b}{bd}=\dfrac{1}{c}[/tex]

Cross multiply:

[tex]\implies c(ad+b)=bd[/tex]

Divide both sides by (ad + b):

[tex]\implies \dfrac{c(ad+b)}{ad+b}=\dfrac{bd}{ad+b}[/tex]

[tex]\implies c=\dfrac{bd}{ad+b}[/tex]

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