What is 11/12 minus 3/8
1 answer:
Answer:
Step-by-step explanation: 11/12 - 3/8
1. First, we will find a common denomenator. It needs to be the least common factor, or the answer will not be in its simplist form. Let's take a look at the multiples of 12 and 8.
12: 12, 24, 36, 48, 60, 72, 84, 96
8: 8, 16, 24, 32, 40, 48, 56, 64, 72
2. Next, we will choose the smallest common multiple. That would be 24.
3. Now, we will work this out.
11/12 = 22/24
3/8 = 9/24
4. Subtract.
22/24 - 9/24
= 13/24
=
I found the denomenators by multiplying.
Hope this answer helped!
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Answer:
The simplest form is x/(x + 3)
Step-by-step explanation:
* To simplify the rational Expression lets revise the factorization
of the quadratic expression
* To factor a quadratic in the form x² ± bx ± c:
- First look at the c term
# If the c term is a positive number, and its factors are r and s they
will have the same sign and their sum is b.
# If the c term is a negative number, then either r or s will be negative
but not both and their difference is b.
- Second look at the b term.
# If the c term is positive and the b term is positive, then both r and
s are positive.
Ex: x² + 5x + 6 = (x + 3)(x + 2)
# If the c term is positive and the b term is negative, then both r and s
are negative.
Ex: x² - 5x + 6 = (x -3)(x - 2)
# If the c term is negative and the b term is positive, then the factor
that is positive will have the greater absolute value. That is, if
|r| > |s|, then r is positive and s is negative.
Ex: x² + 5x - 6 = (x + 6)(x - 1)
# If the c term is negative and the b term is negative, then the factor
that is negative will have the greater absolute value. That is, if
|r| > |s|, then r is negative and s is positive.
Ex: x² - 5x - 6 = (x - 6)(x + 1)
* Now lets solve the problem
- We have two fractions over each other
- Lets simplify the numerator
∵ The numerator is
- Factorize its denominator
∵ The denominator = x² + 2x - 3
- The last term is negative then the two brackets have different signs
∵ 3 = 3 × 1
∵ 3 - 1 = 2
∵ The middle term is +ve
∴ -3 = 3 × -1 ⇒ the greatest is +ve
∴ x² + 2x - 3 = (x + 3)(x - 1)
∴ The numerator =
- Lets simplify the denominator
∵ The denominator is
- Factorize its denominator
∵ The denominator = x² - 2x
- Take x as a common factor and divide each term by x
∵ x² ÷ x = x
∵ -x ÷ x = -1
∴ x² - 2x = x(x - 1)
∴ The denominator =
* Now lets write the fraction as a division
∴ The fraction = ÷
- Change the sign of division and reverse the fraction after it
∴ The fraction =
* Now we can cancel the bracket (x + 2) up with same bracket down
and cancel bracket (x - 1) up with same bracket down
∴ The simplest form =