Given b ≠ a, the fractions \(\cfrac{ax+b}{cx+d}\) and \(\cfrac{b}

1.	Given b ≠ a, the fractions \(\cfrac{ax+b}{cx+d}\) and \(\cfrac{b}d\) are unequal if ……………A) a = c = 1 and x ≠ 0 B) a = b = 0 C) a = c = 0 D) x = 0
Answer» Correct option is (D) x = 0 Let \(\frac{ax+b}{cx+d}\) \(\neq\frac{b}{d}\) \(\Rightarrow\) d (ax+b) \(\neq\) b (x+d) (By cross multiplication) \(\Rightarrow\) adx + bd \(\neq\) bcx + bd \(\Rightarrow\) adx \(\neq\) bcx \(\Rightarrow\) adx - bcx \(\neq\) 0 \(\Rightarrow\) (ad - bc) x \(\neq\) 0 \(\Rightarrow\) ad - bc \(\neq\) 0 and x \(\neq\) 0 \(\Rightarrow\) x \(\neq\) 0 and ad \(\neq\) bc \(\Rightarrow\) x \(\neq\) 0 and d \(\neq\) b if a = c = 1 which is given. Hence, if a = c = 1 and \(x\neq0\) then \(\frac{ax+b}{cx+d}\) and \(\frac{b}{d}\) are unequal. Correct option is D) x = 0

Given b ≠ a, the fractions \(\cfrac{ax+b}{cx+d}\) and \(\cfrac{b}d\) are unequal if ……………A) a = c = 1 and x ≠ 0 B) a = b = 0 C) a = c = 0 D) x = 0

Answer»

Correct option is (D) x = 0

Let \(\frac{ax+b}{cx+d}\) \(\neq\frac{b}{d}\)

\(\Rightarrow\) d (ax+b) \(\neq\) b (x+d) (By cross multiplication)

\(\Rightarrow\) adx + bd \(\neq\) bcx + bd

\(\Rightarrow\) adx \(\neq\) bcx

\(\Rightarrow\) adx - bcx \(\neq\) 0

\(\Rightarrow\) (ad - bc) x \(\neq\) 0

\(\Rightarrow\) ad - bc \(\neq\) 0 and x \(\neq\) 0

\(\Rightarrow\) x \(\neq\) 0 and ad \(\neq\) bc

\(\Rightarrow\) x \(\neq\) 0 and d \(\neq\) b if a = c = 1 which is given.

Hence, if a = c = 1 and \(x\neq0\) then \(\frac{ax+b}{cx+d}\) and \(\frac{b}{d}\) are unequal.

Correct option is D) x = 0