Questions: Find the value of the expression for the given value of (x). [ frac31+frac1x text for x=-frac45 ] (frac31+frac1x=) (square) (square)

Solution Steps

To find the value of the expression \(\frac{3}{1+\frac{1}{x}}\) for \(x = -\frac{4}{5}\), we need to substitute \(x\) into the expression and simplify it step by step.

1. Substitute \(x = -\frac{4}{5}\) into the expression.
2. Simplify the inner fraction \(\frac{1}{x}\).
3. Add the result to 1.
4. Divide 3 by the result from step 3.

We start with the expression: \[ \frac{3}{1 + \frac{1}{x}} \] Substitute \( x = -\frac{4}{5} \): \[ \frac{3}{1 + \frac{1}{-\frac{4}{5}}} \]

Calculate the inner fraction: \[ \frac{1}{-\frac{4}{5}} = -\frac{5}{4} = -1.25 \]

Add 1 to the result from Step 2: \[ 1 + (-1.25) = 1 - 1.25 = -0.25 \]

Finally, divide 3 by the result from Step 3: \[ \frac{3}{-0.25} = -12.0 \]

Final Answer