9)
Rút gọn A
A = $\frac{1}{√x-1}$ + $\frac{√x}{x-1}$
= $\frac{1}{√x-1}$ + $\frac{√x}{(√x-1)(√x+1)}$
= $\frac{√x+1+√x}{(√x-1)(√x+1)}$
= $\frac{2√x+1}{(√x-1)(√x+1)}$
a) Thay x = 49 vào biểu thức B ta có
B = $\frac{49-√49}{2√49+4}$
= $\frac{7}{3}$
b) M = A × B
M = $\frac{2√x+1}{(√x-1)(√x+1)}$ × $\frac{x-√x}{2√x+4}$
= $\frac{2√x+1}{(√x-1)(√x+1)}$ × $\frac{√x(√x-1)}{2√x+4}$
= $\frac{1}{√x+1}$ × $\frac{√x}{4}$
= $\frac{√x}{4√x+4}$
c) $\frac{√x}{4√x+4}$ = $\frac{1}{3}$
⇔ $\frac{√x}{4√x+4}$ = $\frac{1}{3}$
⇔ $\frac{√x}{4√x+4}$ - $\frac{1}{3}$ = 0
⇔ $\frac{3√x-4√x-4}{12√x+12}$ = 0
⇔ $\frac{-√x-4}{12√x+12}$ = 0
⇔ -√x-4 = 0
⇔ x = -16
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