Solve the equation for x: [(1-x)/x] + [x/(1-x)] = 17/4

justaguide | College Teacher | (Level 2) Distinguished Educator

Posted on

We have the equation [(1-x)/x] +[x/ (1+x)] = 17/4 so solve for x.

We notice that 17/4 can be written as 4 + 1/4

So the equation given can be written as

[(1-x)/x] + [x/ (1+x)] = 17/4

=> [(1-x)/x] +[x/ (1+x)] = 4 + 1/4

If we write (1-x)/x = y

=> y + 1/y = 4 + 1/4

we can therefore write y = 4

and also y = 1/4

As y = (1-x) / x

=> (1-x) / x = 4

=> 1-x = 4x

=> x = 1/5

And (1-x) / x = 1/4

=> 4*(1-x) = x

=> 4 – 4x = x

=> 5x = 4

=> x = 4/5

Therefore the possible values of x are 1/5 and 4/5.

neela | High School Teacher | (Level 3) Valedictorian

Posted on

To solve (1-x)/x +x/(1-x) = 17/4

We see that (1-x)/x and x/(1-x) are recprocals. So we put x/(1-x) = t.

Then 1/t+t = 17/4, where t = x/(1-x)

Multiplying by 4t we get:

4t^2+4 = 17t

Therefore 4t^2-17t +4 = 0

(4t - 1)(t-4) = 0. 4t-1 = 0 or t = 1/4 .

So t = 1/4 gives x/(1-x) = 1/4 , Or 4x = 1-x , Or 5x= 1 , x = 1/5.

t-4 = 0 gives t = 4, or  x/(1-x) = 4, x = 4-4x. So  5x= 4, or x = 4/5.

So x= 1/5, Or x =  4/5.