Math Problem Solver

\(\frac{40x^{2}+93x+21}{3x^{3}+16x^{2}-7x-4}\)Solution\(x=\frac{-5+\sqrt{41}}{2},x=\frac{-5-\sqrt{41}}{2},x=-\frac{1}{3}\)Alternative form\(x\approx 0.701562\), \(x\approx -5.70156\), \(x\approx -0.333333\)Step \(\frac{13x+25}{x^{2}+5x-4}+\frac{1}{3x+1}\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{\frac{13x+25}{x^{2}+5x-4}+\frac{1}{3x+1}}\)To find the excluded values, set the denominators equal to \(0\) Step \(x^{2}+5x-4=0\\ 3x+1=0\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x^{2}+5x-4=0}\\ 3x+1=0\)Solve the equation for \(x\)\(\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x=\frac{-5+\sqrt{41}}{2}}\\ \xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x=\frac{-5-\sqrt{41}}{2}}\\ 3x+1=0\)Step \(x=\frac{-5+\sqrt{41}}{2}\\ x=\frac{-5-\sqrt{41}}{2}\\ 3x+1=0\)\(x=\frac{-5+\sqrt{41}}{2}\\ x=\frac{-5-\sqrt{41}}{2}\\ \xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{3x+1}=\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{0}\)Solve the equation for \(x\)\(x=\frac{-5+\sqrt{41}}{2}\\ x=\frac{-5-\sqrt{41}}{2}\\ \xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{x}=\xpmhighlightbox{bgcolor=#D3E3FD, underlinecolor=#D3E3FD}{-\frac{1}{3}}\)S