Factor out the common term \(3\).
\[\frac{5}{3(3x+1)}+9\times \frac{z}{23}+\frac{9\sqrt{6}}{95+x}\times \frac{9}{6(3x+4)}-\frac{x+5oo}{9}\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[\frac{5}{3(3x+1)}+9\times \frac{z}{23}+\frac{9\sqrt{6}}{95+x}\times \frac{9}{6(3x+4)}-\frac{x+5{o}^{2}}{9}\]
Simplify \(9\times \frac{z}{23}\) to \(\frac{9z}{23}\).
\[\frac{5}{3(3x+1)}+\frac{9z}{23}+\frac{9\sqrt{6}}{95+x}\times \frac{9}{6(3x+4)}-\frac{x+5{o}^{2}}{9}\]
Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[\frac{5}{3(3x+1)}+\frac{9z}{23}+\frac{9\sqrt{6}\times 9}{(95+x)\times 6(3x+4)}-\frac{x+5{o}^{2}}{9}\]
Simplify \(9\sqrt{6}\times 9\) to \(81\sqrt{6}\).
\[\frac{5}{3(3x+1)}+\frac{9z}{23}+\frac{81\sqrt{6}}{(95+x)\times 6(3x+4)}-\frac{x+5{o}^{2}}{9}\]
Regroup terms.
\[\frac{5}{3(3x+1)}+\frac{9z}{23}+\frac{81\sqrt{6}}{6(95+x)(3x+4)}-\frac{x+5{o}^{2}}{9}\]
Simplify \(\frac{81\sqrt{6}}{6(95+x)(3x+4)}\) to \(\frac{27\sqrt{6}}{2(95+x)(3x+4)}\).
\[\frac{5}{3(3x+1)}+\frac{9z}{23}+\frac{27\sqrt{6}}{2(95+x)(3x+4)}-\frac{x+5{o}^{2}}{9}\]
Rewrite the expression with a common denominator.
\[\frac{5\times 23\times 2(95+x)(3x+4)\times 9+9z\times 3(3x+1)\times 2(95+x)(3x+4)\times 9+27\sqrt{6}\times 3(3x+1)\times 23\times 9-(x+5{o}^{2})\times 3(3x+1)\times 23\times 2(95+x)(3x+4)}{3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9}\]
Simplify \(5\times 23\times 2(95+x)(3x+4)\times 9\) to \(2070(95+x)(3x+4)\).
\[\frac{2070(95+x)(3x+4)+9z\times 3(3x+1)\times 2(95+x)(3x+4)\times 9+27\sqrt{6}\times 3(3x+1)\times 23\times 9-(x+5{o}^{2})\times 3(3x+1)\times 23\times 2(95+x)(3x+4)}{3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9}\]
Simplify \(9z\times 3(3x+1)\times 2(95+x)(3x+4)\times 9\) to \(486z(3x+1)(95+x)(3x+4)\).
\[\frac{2070(95+x)(3x+4)+486z(3x+1)(95+x)(3x+4)+27\sqrt{6}\times 3(3x+1)\times 23\times 9-(x+5{o}^{2})\times 3(3x+1)\times 23\times 2(95+x)(3x+4)}{3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9}\]
Simplify \(27\sqrt{6}\times 3(3x+1)\times 23\times 9\) to \(16767\sqrt{6}(3x+1)\).
\[\frac{2070(95+x)(3x+4)+486z(3x+1)(95+x)(3x+4)+16767\sqrt{6}(3x+1)-(x+5{o}^{2})\times 3(3x+1)\times 23\times 2(95+x)(3x+4)}{3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9}\]
Simplify \((x+5{o}^{2})\times 3(3x+1)\times 23\times 2(95+x)(3x+4)\) to \(138(x+5{o}^{2})(3x+1)(95+x)(3x+4)\).
\[\frac{2070(95+x)(3x+4)+486z(3x+1)(95+x)(3x+4)+16767\sqrt{6}(3x+1)-138(x+5{o}^{2})(3x+1)(95+x)(3x+4)}{3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9}\]
Factor out the common term \(3\).
\[\frac{3(690(95+x)(3x+4)+162z(3x+1)(95+x)(3x+4)+5589\sqrt{6}(3x+1)-46(x+5{o}^{2})(3x+1)(95+x)(3x+4))}{3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9}\]
Simplify \(3(3x+1)\times 23\times 2(95+x)(3x+4)\times 9\) to \(1242(3x+1)(95+x)(3x+4)\).
\[\frac{3(690(95+x)(3x+4)+162z(3x+1)(95+x)(3x+4)+5589\sqrt{6}(3x+1)-46(x+5{o}^{2})(3x+1)(95+x)(3x+4))}{1242(3x+1)(95+x)(3x+4)}\]
Simplify.
\[\frac{690(95+x)(3x+4)+162z(3x+1)(95+x)(3x+4)+5589\sqrt{6}(3x+1)-46(x+5{o}^{2})(3x+1)(95+x)(3x+4)}{414(3x+1)(95+x)(3x+4)}\]
(690*(95+x)*(3*x+4)+162*z*(3*x+1)*(95+x)*(3*x+4)+5589*sqrt(6)*(3*x+1)-46*(x+5*o^2)*(3*x+1)*(95+x)*(3*x+4))/(414*(3*x+1)*(95+x)*(3*x+4))
