Multiply. Simplify your answer.
1. (n + 3/n- 5) x (n^2 - 5n)
A: n^2 + 3n
2. (6xy^2/2x^2y^6) x (6x^4y^4/9x^3)
A: 2
3. (3h^3 - 6h/10g^2) x (4g/g^2 - 2g)
(There is no typo.)
A: ?
4. (m^2 + m - 2/m^2 - 2m - 8) x (m^2 -8 + 16/3m -3)
(There is no typo.)
A: (m-4)/3
Add or subtract. Simplify your answer.
5. (15)/(2p) - (13)/(2p)
A: 2/2p or p?
6. (3m^2)/(4m^5) + (5m^2)/(4m^5)
A: 2m
7. (x^2 + 8x)/ (x - 2)/ (3x + 14)/ (x - 2)
A: (x + 7)
8. (2t)/(4t^2) + (2)/(t)
A: 10t^2/t^2 or 10?
9. (m^2 - m - 2)/ (m^2 + 6m +5) - (2)/(m + 5)
A: ?
10. (4x)/(x-2) + (3x)/ (2 - x)
A: ?
No one is going to do it for you.
You supposed to try, then ask for help or if you want your answers checked.
I don't know the answers to only three of the expressions I have posted. The rest are the answers that must be checked.
#1 and #2 ok
#3, I agree with you, there is little that can be done
All I could see is to divide top and bottom by 2g
#4 ok
#5, careless error, 2/2p = 1/p , not p
#6 you have a common denominator, so
add them
8m^2/(4m^5) = 2/m^3
#7, according to BEDMAS, division is done in the order it comes,
e.g.
60÷2÷3÷5
=30÷3÷5
= 10÷5
= 2
note 60÷2÷3÷5 = 60/(2x3x5) = 2
so, your question:
(x^2 + 8x)/ (x - 2)/ (3x + 14)/ (x - 2)
= x(x+8)/( (x - 2)(3x + 14)(x - 2) )
that's about it
#8
2t/(4t^2) + 2/t
= 1/2t = 4/2t
= 5/(2t)
#9,
(m^2 - m - 2)/ (m^2 + 6m +5) - (2)/(m + 5)
= (m-2)(m+1)/( (m+1)(m+5) ) - 2/(m+5)
= (m-2)/((m+5) + 2/(m+5)
= m/(m+5)
#10
4x/(x-2) + 3x/(2-x)
= 4x/(x-2) - 3x(x-2)
= x/(x-2)
To solve these multiplication and addition/subtraction problems, we will follow the order of operations and simplify the expressions step by step. Here's how you can solve each problem:
1. (n + 3/n- 5) x (n^2 - 5n)
First, we need to simplify the expression inside the parentheses:
(n + 3) / (n - 5)
Now, we multiply these simplified expressions:
(n + 3) * (n^2 - 5n)
Simplifying further gives us:
n^3 - 2n^2 - 15n
2. (6xy^2/2x^2y^6) x (6x^4y^4/9x^3)
First, simplify each expression inside the parentheses:
(3y^2/x^2) * (2x^4y^4/3x^3)
Next, multiply these simplified expressions:
(3y^2 * 2x^4y^4) / (x^2 * 3x^3)
Now, simplify further by canceling out common factors:
2y^6 / 3x
3. (3h^3 - 6h/10g^2) x (4g/g^2 - 2g)
In this problem, the expression is not clear due to a lack of parentheses. If you can provide the correct placement of parentheses, I can help you solve it.
4. (m^2 + m - 2/m^2 - 2m - 8) x (m^2 -8 + 16/3m -3)
Similar to problem 3, the expression is not clear due to a lack of parentheses. If you can provide the correct placement of parentheses, I can help you solve it.
5. (15)/(2p) - (13)/(2p)
To subtract these fractions, they need a common denominator. In this case, the denominator is already the same:
(15 - 13) / (2p)
Simplifying further:
2 / (2p)
Canceling out the common factor of 2:
1 / p
6. (3m^2)/(4m^5) + (5m^2)/(4m^5)
These fractions already have the same denominator, so we can add them directly:
(3m^2 + 5m^2) / (4m^5)
Simplifying gives us:
8m^2 / (4m^5)
Now, canceling out the common factor of 4:
2m^2 / m^5
Simplifying further:
2/m^3
7. (x^2 + 8x)/ (x - 2)/ (3x + 14)/ (x - 2)
In this problem, there are multiple fractions, and the placement of parentheses makes the expression confusing. Could you please clarify the expression or provide the correct placement of parentheses?
8. (2t)/(4t^2) + (2)/(t)
First, we need to find a common denominator for these fractions, which is 4t^2:
(2t * t) / (4t^2 * t) + (2 * 4t^2) / (4t^2 * t)
Simplifying gives us:
(2t^2) / (4t^3) + (8t^2) / (4t^3)
Combining the fractions:
(2t^2 + 8t^2) / (4t^3)
Simplifying further:
10t^2 / (4t^3)
Canceling out the common factors:
5 / (2t)
9. (m^2 - m - 2)/ (m^2 + 6m + 5) - (2)/(m + 5)
First, let's simplify each fraction:
(m^2 - m - 2) / (m + 5) - (2) / (m + 5)
Combining the fractions now:
[(m^2 - m - 2) - 2] / (m + 5)
Simplifying inside the brackets:
[m^2 - m - 2 - 2] / (m + 5)
[m^2 - m - 4] / (m + 5)
10. (4x)/(x-2) + (3x)/ (2 - x)
First, let's find a common denominator for these fractions, which is (x - 2)(2 - x):
((4x)(2 - x) + (3x)(x - 2)) / ((x - 2)(2 - x))
Expanding and combining the terms:
(8x - 4x^2 + 3x^2 - 6x) / ((x - 2)(2 - x))
Simplifying:
(-4x^2 + 5x) / ((x - 2)(x - 2))
Factoring out the common factor of -x:
-x(4x - 5) / ((x - 2)(x - 2))
This is the simplified answer.
If you have any further questions or need clarification, please let me know!