Question

$$\pi\cdot lim_{x\rightarrow-3}\frac{x+\sqrt{2x+115}}{3x+9}$$

Answer

l<(x+sqrt(2*x+115))/(IM*m*x*(x+3+PI))

Solution


Factor out the common term \(3\).
\[\pi l\imath mx->-3\times \frac{x+\sqrt{2x+115}}{3(x+3)}\]
Cancel \(3\).
\[\pi l\imath mx->-\frac{x+\sqrt{2x+115}}{x+3}\]
Regroup terms.
\[-+\pi l\imath mx>-\frac{x+\sqrt{2x+115}}{x+3}\]
Divide both sides by \(-+\pi \).
\[l\imath mx<\frac{-\frac{x+\sqrt{2x+115}}{x+3}}{-+\pi }\]
Two negatives make a positive.
\[l\imath mx<\frac{\frac{x+\sqrt{2x+115}}{x+3}}{+\pi }\]
Simplify  \(\frac{\frac{x+\sqrt{2x+115}}{x+3}}{+\pi }\)  to  \(\frac{x+\sqrt{2x+115}}{(x+3)+\pi }\).
\[l\imath mx<\frac{x+\sqrt{2x+115}}{(x+3)+\pi }\]
Regroup terms.
\[l\imath mx<\frac{x+\sqrt{2x+115}}{(x+3)+\pi }\]
Convert to common denominators.
\[l\imath mx<\frac{x+\sqrt{2x+115}}{x+3+\pi }\]
Divide both sides by \(\imath \).
\[lmx<\frac{\frac{x+\sqrt{2x+115}}{x+3+\pi }}{\imath }\]
Simplify  \(\frac{\frac{x+\sqrt{2x+115}}{x+3+\pi }}{\imath }\)  to  \(\frac{x+\sqrt{2x+115}}{\imath (x+3+\pi )}\).
\[lmx<\frac{x+\sqrt{2x+115}}{\imath (x+3+\pi )}\]
Divide both sides by \(m\).
\[lx<\frac{\frac{x+\sqrt{2x+115}}{\imath (x+3+\pi )}}{m}\]
Simplify  \(\frac{\frac{x+\sqrt{2x+115}}{\imath (x+3+\pi )}}{m}\)  to  \(\frac{x+\sqrt{2x+115}}{\imath m(x+3+\pi )}\).
\[lx<\frac{x+\sqrt{2x+115}}{\imath m(x+3+\pi )}\]
Divide both sides by \(x\).
\[l<\frac{\frac{x+\sqrt{2x+115}}{\imath m(x+3+\pi )}}{x}\]
Simplify  \(\frac{\frac{x+\sqrt{2x+115}}{\imath m(x+3+\pi )}}{x}\)  to  \(\frac{x+\sqrt{2x+115}}{\imath mx(x+3+\pi )}\).
\[l<\frac{x+\sqrt{2x+115}}{\imath mx(x+3+\pi )}\]