Question

$$lim_{x\rightarrow4}(\frac{3}{4}+\frac{1}{x-5})$$

Answer

l<(4*IM*(3/4+1/(x-5)))/(m*x)

Solution


Regroup terms.
\[-+l\imath mx>4(\frac{3}{4}+\frac{1}{x-5})\]
Divide both sides by \(\imath \).
\[-+lmx>\frac{4(\frac{3}{4}+\frac{1}{x-5})}{\imath }\]
Rationalize the denominator: \(\frac{4(\frac{3}{4}+\frac{1}{x-5})}{\imath } \cdot \frac{\imath }{\imath }=-4(\frac{3}{4}+\frac{1}{x-5})\imath \).
\[-+lmx>-4(\frac{3}{4}+\frac{1}{x-5})\imath \]
Regroup terms.
\[-+lmx>-4\imath (\frac{3}{4}+\frac{1}{x-5})\]
Divide both sides by \(m\).
\[-+lx>-\frac{4\imath (\frac{3}{4}+\frac{1}{x-5})}{m}\]
Divide both sides by \(x\).
\[-+l>-\frac{\frac{4\imath (\frac{3}{4}+\frac{1}{x-5})}{m}}{x}\]
Simplify  \(\frac{\frac{4\imath (\frac{3}{4}+\frac{1}{x-5})}{m}}{x}\)  to  \(\frac{4\imath (\frac{3}{4}+\frac{1}{x-5})}{mx}\).
\[-+l>-\frac{4\imath (\frac{3}{4}+\frac{1}{x-5})}{mx}\]
Multiply both sides by \(-1\).
\[l<\frac{4\imath (\frac{3}{4}+\frac{1}{x-5})}{mx}\]