Question

solve it 1 divided by x minus 1 by x minus 2. equals to 3​

Answer 1

HELLO MATE

1/x - [1/(x-2)] = 3

1 1

--- - ------ = 3

x x-2

The common denominator is x(x-2)

1 x-2 1 x

---• ----- - ----- • --- = 3

x x-2 x-2 x

x-2 x

------- - ------- = 3

x(x-2) x(x-2)

x-2 - x

-------- = 3

x(x-2)

-2 = 3x(x-2)

-2 = 3x2-6x

3x2-6x+2 = 0

Using the quadratic formula we can solve for x

-b±√(b2-4ac)

--------------

2a

6±√[62-4(3)(2)]

-------------------

2(3)

6±√(36-24)

-------------

6

6±√12

-------

6

6±2√3

-------

6

3±√3

------

3

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Answer 2

The solution of the equation is $x=1.577,0.422$.

Step-by-step explanation:

Given : Equation $\frac{1}{x}-\frac{1}{x-2}=3$.

To find : Solve the equation ?

Solution :

Equation $\frac{1}{x}-\frac{1}{x-2}=3$

Solving equation by taking LCM,

$\frac{x-2-x}{x(x-2)}=3$

Cross multiply,

$-2=3x(x-2)$

$-2=3x^2-6x$

$3x^2-6x+2=0$

Using quadratic formula, $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=3, b=-6 and c=2

$x=\frac{-(-6)\pm\sqrt{(-6)^2-4(3)(2)}}{2(3)}$

$x=\frac{6\pm\sqrt{36-24}}{6}$

$x=\frac{6\pm\sqrt{12}}{6}$

$x=\frac{6\pm2\sqrt{3}}{6}$

$x=\frac{3\pm\sqrt{3}}{3}$

$x=\frac{3+\sqrt{3}}{3},\frac{3-\sqrt{3}}{3}$

$x=1.577,0.422$

Therefore, the solution of the equation is $x=1.577,0.422$.

#Learn more

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