Question

CMR: nếu \(\dfrac{a+104}{a-104}=\dfrac{b+105}{b-105}\) thì \(\dfrac{a}{104}=\dfrac{b}{105}\) (với a,b \(\in\) Z và a \(a\ne104;b\ne105\))

Answer 1

Ta có:

\(\dfrac{a+104}{a-104}=\dfrac{a-104+208}{a-104}=1+\dfrac{208}{a-104}=\dfrac{b+105}{b-105}=\dfrac{b-105+210}{b-105}=1+\dfrac{210}{b-105}\)

\(\Rightarrow\dfrac{208}{a-104}=\dfrac{210}{b-105}\)

\(\Rightarrow\dfrac{a-104}{b-105}=\dfrac{208}{210}=\dfrac{104}{105}\)

\(\Rightarrow\dfrac{a-104}{104}=\dfrac{b-105}{105}\)

\(\Rightarrow\dfrac{a}{104}-1=\dfrac{b}{105}-1\)

\(\Rightarrow\dfrac{a}{104}=\dfrac{b}{105}\left(đpcm\right)\)