Answer:
2(d-2)/(2d+1) or 1 - 5/(2d+1)
d can not be -½
Step-by-step explanation:
(d-3)/(2d+1) + (d-1)/(2d+1)
Lcm: 2d+1
(d-3+d-1)/(2d+1)
= (2d-4)/(2d+1)
= 2(d-2)/(2d+1)
If further simplification required:
= (2d-4)/(2d+1)
= (2d+1-5)/(2d+1)
= (2d+1)/(2d+1) - 5/(2d+1)
= 1 - 5/(2d+1)
2d+1 = 0
When d = -½
So d can not be -½ because when the denominator becomes 0, fraction becomes undefined
Answer:
The larger number is -6, the smaller number is -15
Step-by-step explanation:
We have two numbers, a and b.
We know that one number is larger than another by 9.
Then we can write:
a = b + 9
then a is larger than b by 9 units.
If the greater number is increased by 10 (a + 10) and the lesser number is tripled (3*b), the sum of the two would be -41:
(a + 10) + 3*b = -41
So we got two equations:
a = b + 9
(a + 10) + 3*b = -41
This is a system of equations.
One way to solve this is first isolate one variable in one of the two equations:
But we can see that the variable "a" is already isolated in the first equation, so we have:
a = b + 9
now we can replace that in the other equation:
(a + 10) + 3*b = -41
(b + 9) + 10 + 3*b = -41
now we can solve this for b.
9 + b + 10 + 3b = -41
(9 + 10) + (3b + b) = -41
19 + 4b = -41
4b = -41 -19 = -60
b = -60/4 = -15
b = -15
then:
a = b + 9
a = -15 + 9 = -6
a = -6
