Question

6 times a fraction is greater than 7 times its reciprocal by 11. What is the fraction?

Answer 1

Let the fraction = 1/x

6(1/x) - 7(x/1) = 11

6 - 7x² = 11x

7x² + 11x - 6 = 0

7x² + 14x - 3x - 6 = 0

7x(x + 2) -3(x + 2) = 0

(7x - 3)(x + 2) = 0

Either

7x - 3 = 0

7x = 3

x = 3/7

or x + 2 = 0

x = -2

The fraction is 1/x

So the fractions are  7/3 OR -1/2

Answer 2

Answer:

The fraction are 7/3 and -1/2

Step-by-step explanation:

Let the fraction be x.

Thus, the reciprocal is  $\frac{1}{x}$

Now, from the question, we have

$6x=\frac{7}{x}+11\\\\6x^2=7+11x\\6x^2-11x-7=0\\\\x_{1,\:2}=\frac{-\left(-11\right)\pm \sqrt{\left(-11\right)^2-4\cdot \:6\left(-7\right)}}{2\cdot \:6}\\\\x_{1,2}=\frac{11\pm\sqrt{289}}{12}\\\\x_{1,\:2}=\frac{11\pm17}{12}\\\\x=\frac{7}{3},\:x=-\frac{1}{2}$

Therefore, the fraction are 7/3 and -1/2