Question

Find all values of $x$ such that $6= \dfrac{35}{x} -\dfrac{49}{x^2}$. If you find more than one value, then list your solutions in increasing order, separated by commas.

Answer 1

Answer:

$x=\frac{7}{3} , \frac{7}{2}$

Step-by-step explanation:

$6= \frac{35}{x} - \frac{49}{x^2}$

Now we need to solve for x

To get 'x' alone we make the denominators same

LCD = x^2

WE multiply the whole equation by x^2

$6x^2 = 35x - 49$

Now we the equation =0, move all the terms to left hand side

$6x^2-35x + 49=0$

Now we apply quadratic formula to solve for x

a= 6, b= -35 , c= 49

$x= \frac{-b+-\sqrt{b^2-4ac}}{2a}$

$x= \frac{-(-35)+-\sqrt{(-35)^2-4(6)(49)}}{2*6}$

$x= \frac{35+-\sqrt{49}}{12}$

$x= \frac{35+-7}{12}$

Now frame two equations , one with +  and another with -

$x= \frac{35+7}{12}$                                  $x= \frac{35-7}{12}$

$x= \frac{42}{12}$                                       $x= \frac{28}{12}$  

$x= \frac{7}{2}$                                           $x= \frac{7}{3}$  

So value of x= {7/3, 7/2}

Answer 2

X=7/3 and x=7/2

if you want the step-by-step then you just try to isolate x and it is pretty self-explanatory from there on. Hope this helped! 

:P