Find (1/10x−2/3)−(4/5x−1/6) . Write your fractions in simplest form.
To solve the expression (1/10x - 2/3) - (4/5x - 1/6) and write the fractions in simplest form, we first need to simplify each fraction individually.
Let's start with the first fraction: 1/10x. To simplify a fraction, we need to find the greatest common divisor (GCD) of the numerator and the denominator. In this case, the GCD of 1 and 10 is 1. Therefore, we can simplify 1/10 by dividing both the numerator and denominator by 1. This gives us 1/10x.
Next, let's simplify the second fraction: 2/3. The GCD of 2 and 3 is 1, so we cannot simplify this fraction any further.
Now, let's simplify the third fraction: 4/5x. The GCD of 4 and 5 is also 1, so we cannot simplify this fraction any further.
Finally, let's simplify the fourth fraction: 1/6. The GCD of 1 and 6 is also 1, so we cannot simplify this fraction any further.
Now, let's plug these simplified fractions back into the original expression and combine like terms:
(1/10x - 2/3) - (4/5x - 1/6)
Since we have a minus sign between the two fractions, we need to distribute the negative sign to each term in the second fraction:
1/10x - 2/3 - 4/5x + 1/6
Now, to combine like terms, we need to find the least common denominator (LCD) between the fractions with a variable, which is 10x and 5x. The LCD is 10x.
For the first fraction, we need to multiply the numerator and denominator by 1x to make the denominator 10x:
(1 * 1x) / (10x * 1x) - 2/3 - 4/5x + 1/6
This gives us:
x/10x^2 - 2/3 - 4/5x + 1/6
We can simplify the fraction with the variable to:
x/10x^2 - 2/3 - 4/5x + 1/6
Finally, let's combine the fractions with constants:
-2/3 + 1/6 = -4/6 + 1/6 = -3/6
This gives us the final expression:
x/10x^2 - 3/6 - 4/5x
To write it in simplest form:
x/10x^2 - 1/2 - 4/5x