\(\frac{17x+18}{3x^2+x-14}=\frac{a}{x-2}+\frac{b}{3x+7}\)

\(\Rightarrow\frac{17x+18}{3x^2+x-14}=\frac{a\left(3x+7\right)+b\left(x-2\right)}{\left(x-2\right)\left(3x+7\right)}\)

\(\Rightarrow\frac{17x+18}{3x^2+x-14}=\frac{3ax+7a+bx-2b}{3x^2+x-14}\)

\(\Rightarrow\frac{17x+18}{3x^2+x-14}=\frac{3ax+5a+bx}{3x^2+x-14}\)

\(\Rightarrow\frac{17x+18}{3x^2+x-14}=\frac{\left(3a+b\right)x+5a}{3x^2+x-14}\)

Đồng nhất hệ số, ta có: \(\hept{\begin{cases}3a+b=17\\5a=18\end{cases}}\Leftrightarrow\hept{\begin{cases}b=\frac{31}{5}\\a=\frac{18}{5}\end{cases}}\)

ĐKXĐ : \(x\ne\left\{-1;2\right\}\)

\(\frac{x^2+5}{x^3-3x-2}=\frac{a}{x-2}+\frac{b}{\left(x+1\right)^2}\)

\(\Leftrightarrow\frac{x^2+5}{\left(x-2\right)\left(x+1\right)^2}=\frac{a\left(x+1\right)^2+b\left(x-2\right)}{\left(x-2\right)\left(x+1\right)^2}\)

\(\Leftrightarrow\frac{x^2+5}{\left(x-2\right)\left(x+1\right)^2}=\frac{ax^2+2ax+a+bx-2b}{\left(x-2\right)\left(x+1\right)^2}\)

\(\Leftrightarrow\frac{x^2+5}{\left(x-2\right)\left(x+1\right)^2}=\frac{ax^2+x\left(2a+b\right)+\left(a-2b\right)}{\left(x-2\right)\left(x+1\right)^2}\)

Đồng nhất hệ số ta được : \(\hept{\begin{cases}a=1\\2a+b=0\\a-2b=5\end{cases}\Leftrightarrow\hept{\begin{cases}a=1\\b=-2\end{cases}}}\)

Vậy \(a=1;b=-2\)

giúp tớ vs bài này khó wa

Đặt \(B=\frac{2\sqrt{x}+3}{\sqrt{x}-1}=\frac{2\sqrt{x}-2+5}{\sqrt{x}-1}=\frac{2\left(\sqrt{x}-1\right)+5}{\sqrt{x}-1}=2+\frac{5}{\sqrt{x}-1}\)

\(\Rightarrow B\in Z\Leftrightarrow2+\frac{5}{\sqrt{x}-1}\in Z\Leftrightarrow\frac{5}{\sqrt{x}-1}\in Z\Leftrightarrow5⋮\sqrt{x}-1\Leftrightarrow\sqrt{x}-1\inƯ\left(5\right)\)

\(\Rightarrow\sqrt{x}-1\in\left\{-5;-1;1;5\right\}\)

Vì x dương\(\Rightarrow\sqrt{x}-1\ge0\)

\(\Rightarrow\sqrt{x}-1\in\left\{1;5\right\}\)

\(\Rightarrow\sqrt{x}\in\left\{2;6\right\}\)

\(\Rightarrow x\in\left\{4;36\right\}\)

Vậy số phần tử của tập hợp A là 2

\(\frac{x-1}{x+5}=\frac{6}{7}\Leftrightarrow\frac{x-1}{6}=\frac{x+5}{7}\)

\(\Leftrightarrow\frac{7\left(x-1\right)}{42}=\frac{6\left(x+5\right)}{42}\)

\(\Leftrightarrow7\left(x-1\right)=6\left(x+5\right)\)

\(\Leftrightarrow7x-7=6x+30\)

\(\Leftrightarrow7x-6x=7+30\)

\(\Leftrightarrow x=37\)

Vậy nghiệm của phương trình là x = 37