Question

question evaluate the limit: $limlimits_{x \to 1} \frac{4x - 7}{\frac{5}{3} - \frac{3x - 1}{x + 5}}$ answer attempt 1 out of 2 input box submit answer dne

Explanation:

Step1: Simplify the denominator

First, we simplify the denominator \(\frac{5}{3}-\frac{3x - 1}{x + 5}\). Find a common denominator, which is \(3(x + 5)\).

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Step2: Rewrite the original limit

Now the original limit \(\lim_{x
ightarrow1}\frac{4x - 7}{\frac{5}{3}-\frac{3x - 1}{x + 5}}\) becomes \(\lim_{x
ightarrow1}\frac{4x - 7}{\frac{-4(x - 7)}{3(x + 5)}}\). When dividing by a fraction, we multiply by its reciprocal:

$$ \lim_{x ightarrow1}\frac{(4x - 7)\times3(x + 5)}{-4(x - 7)} $$

Step3: Substitute \(x = 1\)

Now we substitute \(x = 1\) into the expression \(\frac{3(4x - 7)(x + 5)}{-4(x - 7)}\):

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Answer:

\(-\frac{9}{4}\)