Đáp án:
`a, S={-3/5}`
`b, S={7/2,1/3}`
`c,` `Pt` `vô` `số` `nghiệm.`
Giải thích các bước giải:
`a, (x^2 + 1) . (5x + 3)=0`
`<=>`\(\left[ \begin{array}{l}x^2+1=0\\5x+3=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x∈∅\\x=\frac{-3}{5}\end{array} \right.\)
`KL:` `S={-3/5}`
`b, (2x - 7)^2 - (4x +5) . (7 - 2x) = 0`
`<=> (2x-7)^2+(4x-5).(-(2x-7))=0`
`<=> (2x-7)(2x-7-(-4x-5))=0`
`<=> (2x-7).(2x-7+4x+5)=0`
`<=> (2x-7)(6x-2)`
`<=>`\(\left[ \begin{array}{l}2x-7=0\\3x-1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=\frac{7}{2}\ \\x=\frac{1}{3} \end{array} \right.\)
`KL:` `S={7/2,1/3}`
`c, (x - 2)/(x-1) + (x+2)/(x +1) = (2( 2 - x^2)) / (1 - x^2) (ĐK: x \ne ±1)`
`<=> (x - 2)/(x-1) + (x+2)/(x +1) = (4-2x^2) / (1 - x^2)`
`<=> (x - 2)/(x-1) + (x+2)/(x +1) - (4-2x^2) / (1 - x^2)=0`
`<=> (x - 2)/(x-1) + (x+2)/(x +1) + (4-2x^2) / ((x-1)(x+1))=0`
`<=> ((x+1)(x-2)+(x-1)(x+2)+4-2x^2) / ((x-1)(x+1))`
`<=> 0 / ((x-1)(x+1))=0`
`<=> 0=0`
`Vậy` `pt` `vô` `số` `nghiệm.`
