Answer:
Step-by-step explanation:
Rationalize the denominator of b. So, multiply the numerator and denominator by [tex]\sqrt{x}[/tex]
[tex]b = \frac{(1-2\sqrt{x}) *\sqrt{x}}{\sqrt{x}*\sqrt{x} }=\frac{1*\sqrt{x} -2\sqrt{x} *\sqrt{x} }{\sqrt{x} *\sqrt{x} }\\\\=\frac{\sqrt{x} -2x}{x}\\[/tex]
Now, find a +b
[tex]a +b = \frac{2x+\sqrt{x} }{x}+\frac{\sqrt{x} -2x}{x}\\\\=\frac{2x+\sqrt{x} +\sqrt{x} -2x}{x}[/tex]
Combine like terms
[tex]= \frac{2x-2x+\sqrt{x} +\sqrt{x} }{x}\\\\=\frac{2\sqrt{x} }{x}[/tex]
Now find (a + b)²
(a +b)² = [tex](\frac{2\sqrt{x} }{x})^{2}[/tex]
[tex]= \frac{2^{2}*(\sqrt{x} )^{2}}{x^{2}}\\\\= \frac{4* x}{x^{2}}\\\\= \frac{4}{x}[/tex]
Hint: [tex]\sqrt{x} *\sqrt{x} =\sqrt{x*x}=x[/tex]
