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jjjoooorrrrddddaannn
26.10.2020 •
Mathematics
The numerator of a fraction is 1 less than the denominator.
When both numerator and denominator are increased by 2,
the fraction is increased by . Find the original fraction.
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Ответ:
There is missing data in the problem, I have added it to solve the problem. You can use your real data once you understand the explanation.
Original fraction:
Step-by-step explanation:
The numerator of a fraction is 1 less than the denominator and when both parts are increased by 2, the value of the fraction increases by 1/24. Find the original fraction.
Let's call:
x=original numerator
x+1=original denominator
x+2=increased numerator
x+3=increased denominator
Original fraction:
Increased fraction:
The difference between both is 1/24:
Multiply by (x+3)(x+1):
Simplifying each fraction when possible:
Operating:
Simplifying:
Multiplying by 24:
Rearranging:
Factoring:
We have two solutions:
Selecting the first solution:
Original fraction:
Increased fraction:
The difference between both is:
This is a valid solution
Selecting the second solution:
Original fraction:
Increased fraction:
The difference between both is:
This solution is only valid if we express the fractions with their negative values. When we simplify them, the first condition is not met. Thus, the solutions are:
Original fraction:
Note: The last solution can be arguable because the real simplified fraction is not a solution. My opinion is that it's valid as long as it's expressed with their original signs.
Ответ:
147 square feet