Question

The sum of the reciprocals of 3 - x and 1 - 2x is 6 times the reciprocal of 3 - 4x. Find the value of x.

Answer 1

Answer:
`(6)/(17)`

Explanation:

Reciprocal of
`3-x\ \text{is}\ (1)/(3-x)`

Reciprocal of
`1-2x\ \text{is}\ (1)/(1-2x)`

According to question

`\Rightarrow (1)/(3-x)+(1)/(1-2x)=6* (1)/(3-4x)\\\\\Rightarrow ((1-2x)+(3-x))/((1-2x)(3-x))=(6)/(3-4x)\\\\\Rightarrow (4-3x)/((1-2x)(3-x))=(6)/(3-4x)`

`\Rightarrow (4-3x)(3-4x)=6(1-2x)(3-x)\\\Rightarrow 12-16x-9x+12x^2=18-6x-36x+12x^2\\\Rightarrow 12x^2-25x+12=18-42x+12x^2=0\\\Rightarrow 42x-25x=6\\\Rightarrow 17x=6\\\Rightarrow x=(6)/(17)`