Answer:
[tex]x=\frac{ab}{a+b}[/tex]
Step-by-step explanation:
Combine the two fractions on the right by using the common denominator ab.
[tex]\frac{1}{x}=\frac{b}{ab}+\frac{a}{ab}\\=\frac{b+a}{ab}[/tex]
If two quantities are equal, then their reciprocals are equal.
[tex]x=\frac{ab}{b+a}[/tex]
Answer:
x = [tex]\frac{ab}{b+a}[/tex]
Step-by-step explanation:
Given
[tex]\frac{1}{x}[/tex] = [tex]\frac{1}{a}[/tex] + [tex]\frac{1}{b}[/tex]
Multiply through by abx ( the LCM of denominators ) to clear the fractions
ab = bx + ax ← factor out x from each term on the left side
ab = x(b + a) ← divide both sides by (b + a)
[tex]\frac{ab}{b+a}[/tex] = x
