First, we need to clear the denominators by multiplying both sides of the equation by the common denominator of x(x+2):
1/x + 1/(x+2) = 9/40
40x(x+2)(1/x) + 40x(x+2)(1/(x+2)) = 40x(x+2)(9/40)
40(x+2) + 40x = 9x(x+2)
Distribute the 40 on the left:
40x + 80 + 40x = 9x(x+2)
Combine like terms:
80x + 80 = 9x^2 + 18x
Move all terms to one side:
9x^2 - 62x - 80 = 0
Now we can factor this quadratic equation:
(9x + 8)(x - 10) = 0
Setting each factor equal to zero gives us two possible solutions:
9x + 8 = 0 or x - 10 = 0
Solving for x gives us:
x = -8/9 or x = 10
We can disregard the negative solution since we are looking for even integers. Thus, the two consecutive even integers are:
x = 10
x+2 = 12
Therefore, the two consecutive even integers are 10 and 12.
The sum of the reciprocals of two consecutive even integers is 9/40. This can be represented by the equation shown. 1/x+1/x+2=9/40
use the rational equation to determine the integers. show all work
3 answers
your wrong
I apologize for the error in my previous answer. Here is the correct solution:
The equation is:
1/x + 1/(x+2) = 9/40
To solve for x, we can cross multiply and simplify:
40(x+2) + 40x = 9x(x+2)
80x + 80 = 9x^2 + 18x
9x^2 - 62x - 80 = 0
We can factor the quadratic equation:
(9x + 4)(x - 10) = 0
Setting each factor equal to zero gives us two possible solutions:
9x + 4 = 0 or x - 10 = 0
Solving for x gives us:
x = -4/9 or x = 10
Since we are looking for consecutive even integers, x must be even. Thus, we can disregard the solution x = -4/9. The only valid solution is x = 10.
Therefore, the two consecutive even integers are:
x = 10
x+2 = 12
Hence, the two consecutive even integers that satisfy the given condition are 10 and 12.
The equation is:
1/x + 1/(x+2) = 9/40
To solve for x, we can cross multiply and simplify:
40(x+2) + 40x = 9x(x+2)
80x + 80 = 9x^2 + 18x
9x^2 - 62x - 80 = 0
We can factor the quadratic equation:
(9x + 4)(x - 10) = 0
Setting each factor equal to zero gives us two possible solutions:
9x + 4 = 0 or x - 10 = 0
Solving for x gives us:
x = -4/9 or x = 10
Since we are looking for consecutive even integers, x must be even. Thus, we can disregard the solution x = -4/9. The only valid solution is x = 10.
Therefore, the two consecutive even integers are:
x = 10
x+2 = 12
Hence, the two consecutive even integers that satisfy the given condition are 10 and 12.