Question

$$\frac { \sqrt { x + 1 } + \sqrt { x - 1 } } { \sqrt { x + 1 } - \sqrt { x - 1 } } = \frac { 1 } { 2 }$$

Answer

$$q=(11+sqrt(x))/(e^2*IM*u^2*a*t*o^3*n^2*b*y*c*m*p*sqrt(x)*sin(g))$$

Solution


Regroup terms.
\[quuatooonnbycmp\sqrt{x}e\imath (\sin{g})e+1+\sqrt{x}-1\times \sqrt{x}+1-\sqrt{x}-1=12\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[q{u}^{1+1}at{o}^{1+1+1}{n}^{1+1}bycmp\sqrt{x}e\imath (\sin{g})e+1+\sqrt{x}-1\times \sqrt{x}+1-\sqrt{x}-1=12\]
Simplify  \(1+1\)  to  \(2\).
\[q{u}^{2}at{o}^{2+1}{n}^{2}bycmp\sqrt{x}e\imath (\sin{g})e+1+\sqrt{x}-1\times \sqrt{x}+1-\sqrt{x}-1=12\]
Simplify  \(2+1\)  to  \(3\).
\[q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}e\imath (\sin{g})e+1+\sqrt{x}-1\times \sqrt{x}+1-\sqrt{x}-1=12\]
Use Product Rule: \({x}^{a}{x}^{b}={x}^{a+b}\).
\[q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}{e}^{2}\imath \sin{g}+1+\sqrt{x}-1\times \sqrt{x}+1-\sqrt{x}-1=12\]
Regroup terms.
\[{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}+1+\sqrt{x}-1\times \sqrt{x}+1-\sqrt{x}-1=12\]
Simplify  \(1\times \sqrt{x}\)  to  \({x}^{\frac{1}{2}}\).
\[{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}+1+\sqrt{x}-{x}^{\frac{1}{2}}+1-\sqrt{x}-1=12\]
Convert \({x}^{\frac{1}{2}}\) to square root.
\[{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}+1+\sqrt{x}-\sqrt{x}+1-\sqrt{x}-1=12\]
Simplify  \({e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}+1+\sqrt{x}-\sqrt{x}+1-\sqrt{x}-1\)  to  \({e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}+1-\sqrt{x}\).
\[{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}+1-\sqrt{x}=12\]
Subtract \(1\) from both sides.
\[{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}-\sqrt{x}=12-1\]
Regroup terms.
\[-\sqrt{x}+{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=12-1\]
Simplify  \(12-1\)  to  \(11\).
\[-\sqrt{x}+{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=11\]
Add \(\sqrt{x}\) to both sides.
\[{e}^{2}\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=11+\sqrt{x}\]
Divide both sides by \({e}^{2}\).
\[\imath q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}}\]
Divide both sides by \(\imath \).
\[q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}}}{\imath }\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}}}{\imath }\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath }\).
\[q{u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath }\]
Divide both sides by \({u}^{2}\).
\[qat{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath }}{{u}^{2}}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath }}{{u}^{2}}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}}\).
\[qat{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}}\]
Divide both sides by \(a\).
\[qt{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}}}{a}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}}}{a}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}a}\).
\[qt{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}a}\]
Divide both sides by \(t\).
\[q{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}a}}{t}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}a}}{t}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at}\).
\[q{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at}\]
Divide both sides by \({o}^{3}\).
\[q{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at}}{{o}^{3}}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at}}{{o}^{3}}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}}\).
\[q{n}^{2}bycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}}\]
Divide both sides by \({n}^{2}\).
\[qbycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}}}{{n}^{2}}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}}}{{n}^{2}}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}}\).
\[qbycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}}\]
Divide both sides by \(b\).
\[qycmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}}}{b}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}}}{b}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}b}\).
\[qycmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}b}\]
Divide both sides by \(y\).
\[qcmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}b}}{y}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}b}}{y}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}by}\).
\[qcmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}by}\]
Divide both sides by \(c\).
\[qmp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}by}}{c}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}by}}{c}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}byc}\).
\[qmp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}byc}\]
Divide both sides by \(m\).
\[qp\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}byc}}{m}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}byc}}{m}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycm}\).
\[qp\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycm}\]
Divide both sides by \(p\).
\[q\sqrt{x}\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycm}}{p}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycm}}{p}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp}\).
\[q\sqrt{x}\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp}\]
Divide both sides by \(\sqrt{x}\).
\[q\sin{g}=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp}}{\sqrt{x}}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp}}{\sqrt{x}}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}}\).
\[q\sin{g}=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}}\]
Divide both sides by \(\sin{g}\).
\[q=\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}}}{\sin{g}}\]
Simplify  \(\frac{\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}}}{\sin{g}}\)  to  \(\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}}\).
\[q=\frac{11+\sqrt{x}}{{e}^{2}\imath {u}^{2}at{o}^{3}{n}^{2}bycmp\sqrt{x}\sin{g}}\]