Đáp án+Giải thích các bước giải:
`1) (x+1)/(x-1)-(x-1)/(x+1)=4/(x^2-1) (ĐKXĐ: x\ne±1)`
`<=> ((x+1)^2)/(x^2-1)-((x-1)^2)/(x^2-1)=4/(x^2-1)`
`=> x^2+2x+1-x^2+2x-1=4`
`<=> 4x =4`
`<=> x =1(KTM)`
Vậy phương trình `1)` vô nghiệm
`2) (x+4)/(x-1)+(x-1)/(x+1)=(16)/(x^2-1)(ĐKXĐ: x\ne±1)`
`<=> ((x+4)(x+1))/(x^2-1)+((x-1)^2)/(x^2-1)=(16)/(x^2-1)`
`=> x^2+5x+4+x^2-2x+1-16=0`
`<=> 2x^2+3x-11=0`
`<=> x^2+3/2x-(11)/2=0`
`<=> x^2+2. x . 3/4 +9/(16)-(97)/(16)=0`
`<=> (x+3/4)^2=(\sqrt{97})/(16)`
`<=>`\(\left[ \begin{array}{l}x+ \dfrac{3}{4}= \dfrac{\sqrt{97}}{16}\\x+ \dfrac{3}{4}= -\dfrac{\sqrt{97}}{16}\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x= \dfrac{\sqrt{97}}{16}-\dfrac{3}{4}(t/m)\\x= \dfrac{-\sqrt{97}}{16}-\dfrac{3}{4}(t/m)\end{array} \right.\)
`3) x(2x-9)=3x(x-5)`
`<=> 2x^2-9x = 3x^2 - 15x`
`<=> x^2-6x=0`
`<=> x(x-6)=0`
`<=>` \(\left[ \begin{array}{l}x=0\\x-6=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=0\\x=6\end{array} \right.\)
`4) 0,5x(x-3)=(x-3)(1,5x-1)`
`<=>0,5x(x-3)-(x-3)(1,5x-1)=0`
`<=> 0,5x^2-1,5x-(1,5x^2-5,5x+3)=0`
`<=> 0,5x^2-1,5x-1,5x^2+5,5x-3=0`
`<=> -x^2+4x-3=0`
`<=> x^2-4x+3=0`
`<=>(x-3)(x-1)=0`
`<=>`\(\left[ \begin{array}{l}x-3=0\\x-1=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=3\\x=1\end{array} \right.\)
`5) 3/7x-1=1/7x(3x-7)`
`<=> 3/7x-1-1/7x(3x-7)=0`
`<=> 3/7x-1-3/7x^2+x=0`
`<=> -3/7x^2+(10)/7x-1=0`
`<=> (3/7x-1)(1-x)=0`
`<=>` \(\left[ \begin{array}{l}\dfrac{3}{7}x-1=0\\1-x=0\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}\dfrac{3}{7}x=1\\x=1\end{array} \right.\)
`<=>` \(\left[ \begin{array}{l}x=\dfrac{7}{3}\\x=1\end{array} \right.\)
`6) 8x(3x-5)=6(3x-7)`
`<=> 8x(3x-5)-6(3x-7)=0`
`<=> 24x^2-40x - 18x+42=0`
`<=> 24x^2-58x+42=0`
`<=> 4x^2-(29)/3x+7=0`
`<=> (2x)^2-2.2x.(29)/(12)+(841)/(144)+(167)/(144)=0`
`<=> (2x-(29)/(12))^2=-(167)/(144)`(vô nghiệm)
Vậy phương trình `6)` vô nghiệm
