Solving an Equation with Incomplete Image Clarity
The image is not entirely clear, but I will provide the solution to the equation based on what is visible:
Given:
\[ \frac{1}{a} + \frac{1}{b} = \frac{1}{4.5} \]
First, find the common denominator for \(\frac{1}{a}\) and \(\frac{1}{b}\), which is \(ab\).
\[ \frac{b}{ab} + \frac{a}{ab} = \frac{1}{4.5} \]
\[ \frac{a + b}{ab} = \frac{1}{4.5} \]
Cross-multiply to solve for \(a + b\):
\[ a + b = ab \cdot \frac{1}{4.5} \]
Convert 4.5 to a fraction:
\[ a + b = ab \cdot \frac{1}{\frac{9}{2}} \]
Inverse the fraction:
\[ a + b = ab \cdot \frac{2}{9} \]
Divide both sides by ab to solve for \(\frac{1}{ab}\):
\[ \frac{a+b}{ab} = \frac{2}{9} \]
Therefore:
\[ \frac{1}{ab} = \frac{2}{9(a+b)} \]
The correct expression that represents \(\frac{1}{ab}\) is:
\[ \frac{2}{9(a+b)} \]
Looking at the options provided, the answer is:
b) \(\frac{2}{9(a+b)}\)
