Question

Giải phương trình sau: (x-1)(x+5)/3 - (x+2)(x+5)/12 = (x-1)(x+2)/4

Answer 1

\(\frac{\left(x-1\right)\left(x+5\right)}{3}-\frac{\left(x+2\right)\left(x+5\right)}{12}=\frac{\left(x-1\right)\left(x+2\right)}{4}\)

⇔4(x²+4x-5)-(x+2)(x+5)=3(x²+x-2)

⇔4x²+16x-20-x²-7x-10=3x²+3x-6

⇔4x²-x²-3x²+16x-7x-3x=-6+10+20

⇔6x=24

⇔x=4

Vậy phương trình có nghiệm là x=4

Answer 2

\(\frac{\left(x+1\right)\left(x+5\right)}{3}-\frac{\left(x+2\right)\left(x+5\right)}{12}=\frac{\left(x-1\right)\left(x+2\right)}{4}\)

⇔4(x+1)(x+5)-(x+2)(x+5)=3(x-1)(x+2)

⇔4x²+24x+20-x²-7x-10=3x²+3x-6

⇔4x²+24x-x²-7x-3x²-3x=-6-20+10

⇔14x=-16

⇔x=\(\frac{-8}{7}\)

Vậy phương trình có nghiệm là x=\(\frac{-8}{7}\)