Question

giả phương trình \(\dfrac{144}{x+2}\) - \(\dfrac{100}{x}\)= 2

Answer 1

ĐKXĐ: x\(\ne-2\)

Ta có: \(\dfrac{144}{x+2}-\dfrac{100}{x}=2\)

<=> \(\dfrac{144x}{\left(x+2\right)x}-\dfrac{100\left(x+2\right)}{\left(x+2\right)x}=\dfrac{2\left(x+2\right)x}{\left(x+2\right)x}\)

=> 144x-100(x+2)=2(x+2)x

<=> 144x-100x-200=2x²+4x

<=> 44x-4x-2x²-200=0

<=> 40x-2x²-200=0

<=> 2(20x-x²-100)=0

=> 20x-x²-100=0

<=> -(x-10)²=0

=> (x-10)²=0

<=> x-10=0

<=> x=10 (thỏa mãn ĐKXĐ)

Vậy S=\(\left\{10\right\}\)