+0

# math problem

0
107
1

Levans writes a positive fraction in which the numerator and denominator are integers, and the numerator is $$2$$ greater than the denominator. He then writes several more fractions. To make each new fraction, he increases both the numerator and the denominator of the previous fraction by $$1$$. He then multiplies all his fractions together. He has $$3$$ fractions, and their product equals $$10$$. What is the value of the first fraction he wrote?

May 19, 2022

#1
+2448
0

We have the equation: $$\large{{{x +2} \over x} \times {x+3 \over x+1} \times {x+4 \over x+2} = 10}$$

Because there is the term $$x+2$$ in both the numerator and the denominator, we can cancel them out.

This gives us: $$\large{{x+3 \over x+1} \times {x+4 \over x} = 10 }$$

Simplifying the left-hand side gives us: $$\large{{{x^2 + 7x + 12} \over {x^2 + x}} = 10 }$$

From the equation, we know that the numerator ($$x^2 + 7x + 12$$) must be 10 times the denominator ($$x^2 + x$$)

Thus, we have: $$10(x^2 +x) = x^2 + 7x + 12$$

Now, we have to solve the equation, and subsitute our values into the first fraction ($$\large{x+2 \over x}$$)

Can you take it from here?

May 19, 2022
edited by BuilderBoi  May 19, 2022