Rewrite \(25-{x}^{2}\) in the form \({a}^{2}-{b}^{2}\), where \(a=5\) and \(b=x\).
\[l\imath mx->-4\times \frac{3-\sqrt{{5}^{2}-{x}^{2}}}{x+4}\]
Use Difference of Squares: \({a}^{2}-{b}^{2}=(a+b)(a-b)\).
\[l\imath mx->-4\times \frac{3-\sqrt{(5+x)(5-x)}}{x+4}\]
Simplify \(4\times \frac{3-\sqrt{(5+x)(5-x)}}{x+4}\) to \(\frac{4(3-\sqrt{(5+x)(5-x)})}{x+4}\).
\[l\imath mx->-\frac{4(3-\sqrt{(5+x)(5-x)})}{x+4}\]
Regroup terms.
\[-+l\imath mx>-\frac{4(3-\sqrt{(5+x)(5-x)})}{x+4}\]
Divide both sides by \(\imath \).
\[-+lmx>-\frac{\frac{4(3-\sqrt{(5+x)(5-x)})}{x+4}}{\imath }\]
Simplify \(\frac{\frac{4(3-\sqrt{(5+x)(5-x)})}{x+4}}{\imath }\) to \(\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath (x+4)}\).
\[-+lmx>-\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath (x+4)}\]
Divide both sides by \(m\).
\[-+lx>-\frac{\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath (x+4)}}{m}\]
Simplify \(\frac{\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath (x+4)}}{m}\) to \(\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath m(x+4)}\).
\[-+lx>-\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath m(x+4)}\]
Divide both sides by \(x\).
\[-+l>-\frac{\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath m(x+4)}}{x}\]
Simplify \(\frac{\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath m(x+4)}}{x}\) to \(\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath mx(x+4)}\).
\[-+l>-\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath mx(x+4)}\]
Multiply both sides by \(-1\).
\[l<\frac{4(3-\sqrt{(5+x)(5-x)})}{\imath mx(x+4)}\]
l<(4*(3-sqrt((5+x)*(5-x))))/(IM*m*x*(x+4))
