b, - ĐKXĐ : \(\left\{{}\begin{matrix}x-2\ne0\\x+2\ne0\end{matrix}\right.\) => \(\left\{{}\begin{matrix}x\ne2\\x\ne-2\end{matrix}\right.\)
Ta có : \(\frac{5x}{x^2-4}-\frac{4}{x+2}=\frac{5}{x-2}\)
=> \(\frac{5x}{x^2-4}-\frac{4\left(x-2\right)}{x^2-4}=\frac{5\left(x+2\right)}{x^2-4}\)
=> \(5x-4\left(x-2\right)=5\left(x+2\right)\)
=> \(5x-4x+8=5x+10\)
=> \(5x-4x-5x=10-8\)
=> \(-4x=2\)
=> \(x=-\frac{1}{2}\) ( TM )
Vậy phương trình trên có tập nghiệm là \(S=\left\{-\frac{1}{2}\right\}\)
c, Ta có : \(x^4-15x^2+56=0\)
=> \(\left(x^2\right)^2-\frac{2.x^2.15}{2}+\frac{225}{4}-\frac{1}{4}=0\)
=> \(\left(x^2-\frac{15}{2}\right)^2=\frac{1}{4}\)
=> \(\left[{}\begin{matrix}x^2-\frac{15}{2}=\sqrt{\frac{1}{4}}\\x^2-\frac{15}{2}=-\sqrt{\frac{1}{4}}\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x^2=\sqrt{\frac{1}{4}}+\frac{15}{2}=8\\x^2=-\sqrt{\frac{1}{4}}+\frac{15}{2}=7\end{matrix}\right.\)
=> \(\left[{}\begin{matrix}x=\sqrt{8}\\x=-\sqrt{8}\\x=\sqrt{7}\\x=-\sqrt{7}\end{matrix}\right.\)
Vậy phương trình trên có tập nghiệm là \(S=\left\{\sqrt{8};-\sqrt{8};\sqrt{7};-\sqrt{7}\right\}\)
a)
\(\frac{x-5x-1}{6}=\frac{8-3x}{4}\)
\(\Leftrightarrow\frac{4x-20x-4}{24}=\frac{48-18x}{24}\)
\(\Leftrightarrow\frac{-16x-4}{24}=\frac{48-18x}{24}\)
\(\Leftrightarrow\frac{-16x-4-48+18x}{24}=0\)
\(\Leftrightarrow\frac{2x-52}{24}=0\)
\(\Rightarrow2x-52=0\)
\(x=\frac{52}{2}=26\)