Answer: 7/8
Step-by-step explanation:
The easiest way to do this is to find a common denominator, so first we find out 2 times how much equals 8? 2x4 = 8. So with 8 being our common denominator, we have to multiple 4 to every number in the fraction 1/2. So 1x4 = (4/8) = 2x4. Then you just add the top numbers, so 4 + 3 = 7 and keep the denominator. 7/8.
Answer:
31
Step-by-step explanation:
Step-by-step explanation:
<h3>Appropriate Question :-</h3>
Find the limit
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)

Given expression is
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
On substituting directly x = 1, we get,


which is indeterminant form.
Consider again,
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D)
can be rewritten as
![\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 3x + 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20%7Bx%7D%5E%7B2%7D%20-%203x%20%2B%202%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( {x}^{2} - 2x - x + 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20%7Bx%7D%5E%7B2%7D%20-%202x%20-%20x%20%2B%202%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x( x(x - 2) - 1(x - 2))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28%20x%28x%20-%202%29%20-%201%28x%20-%202%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x(x - 1)}-\dfrac{1}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%28x%20-%201%29%7D-%5Cdfrac%7B1%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ {(x - 2)}^{2} - 1}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%7B%28x%20-%202%29%7D%5E%7B2%7D%20-%201%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 2 - 1)(x - 2 + 1)}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%202%20-%201%29%28x%20-%202%20%2B%201%29%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)(x - 1)}{x(x - 2) \: (x - 1))}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%203%29%28x%20-%201%29%7D%7Bx%28x%20-%202%29%20%5C%3A%20%28x%20-%201%29%29%7D%5Cright%5D)
![\rm \: = \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{ (x - 3)}{x(x - 2)}\right]](https://tex.z-dn.net/?f=%5Crm%20%5C%3A%20%3D%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7B%20%28x%20-%203%29%7D%7Bx%28x%20-%202%29%7D%5Cright%5D)



Hence,
![\rm\implies \:\boxed{ \rm{ \:\rm \: \sf {\displaystyle{\lim_{x\to 1}}} \: \left[\dfrac{x-2}{x^2-x}-\dfrac{1}{x^3-3x^2+2x}\right] = 2 \: }}](https://tex.z-dn.net/?f=%5Crm%5Cimplies%20%5C%3A%5Cboxed%7B%20%5Crm%7B%20%5C%3A%5Crm%20%5C%3A%20%5Csf%20%7B%5Cdisplaystyle%7B%5Clim_%7Bx%5Cto%201%7D%7D%7D%20%5C%3A%20%5Cleft%5B%5Cdfrac%7Bx-2%7D%7Bx%5E2-x%7D-%5Cdfrac%7B1%7D%7Bx%5E3-3x%5E2%2B2x%7D%5Cright%5D%20%3D%202%20%5C%3A%20%7D%7D)

Answer:
The answer is 3.
Step-by-step explanation:
7.55-6.50=1.05
1.05/.35=3
The answer is 5/3 can I have the some points