Question

5 phần x+2 bằng 6 phần x-3

Answer 1

=>5(x-3)=6(x+2)

=>6x+12=5x-15

=>x=-27

Answer 2

\(\dfrac{5}{x+2}=\dfrac{6}{x-3}\) (ĐK: \(x\ne-2;x\ne3\))

\(\Rightarrow5\left(x-3\right)=6\left(x+2\right)\)

\(\Leftrightarrow5x-15=6x+12\)

\(\Leftrightarrow-15-12=6x-5x\)

\(\Leftrightarrow-27=x\)

\(\Leftrightarrow x=-27\) (TMĐK)

Vậy \(S=\left\{-27\right\}\).

Answer 3

\(\dfrac{5}{x+2}=\dfrac{6}{x-3}\text{ĐKXĐ:}x\ne-2;3\)

\(\Leftrightarrow\dfrac{5\left(x-3\right)}{\left(x+2\right)\left(x-3\right)}=\dfrac{6\left(x+2\right)}{\left(x+2\right)\left(x-3\right)}MTC:\left(x+2\right)\left(x-3\right)\)

\(\Rightarrow5x-15=6x+12\)

\(\Leftrightarrow5x-15-6x-12=0\)

\(\Leftrightarrow-27-x=0\)

\(\Leftrightarrow x=-27\)

\(\text{Vậy phương trình có tập nghiệm là }S=\left\{-27\right\}\)