I have the equation $$x = \frac{y+y}{\frac{y}{70} + \frac{y}{90}} $$ and I need to solve for x. My calculator has already shown me that it's not necessary to know y to solve this equation, but I can't seem to figure it out. This is how I try to solve it:
$$
x = \frac{y+y}{\frac{y}{70} + \frac{y}{90}} = 2y\left(\frac{70}{y} + \frac{90}{y}\right) = 2y\left(\frac{90+70}{y}\right) = 2y\cdot\frac{160}{y} = \frac{320y}{y} = 320
$$
But according to my calculator, this is not correct. The answer should be 78.75, but I don't know why. Any help would be much appreciated.
[Math] Simplifying nested/complex fractions with variables
algebra-precalculusfractionsproblem solving
Best Answer
When manipulating expressions, the most important thing is to think small. Find the smallest part of the expression you can do something with. In this case,
$$\frac{2y}{\frac{y}{70}+\frac{y}{90}}$$
has as the smallest available task add the fractions on the bottom, which gives (only showing that part)
$$\frac{y}{70}+\frac{y}{90}=\frac{90y+70y}{70\cdot 90}=\frac{160y}{6300}=\frac{8y}{315}$$
Putting that back in, we now have
$$\frac{2y}{\left(\frac{8y}{315}\right)}=2y\left(\frac{315}{8y}\right)=\frac{630y}{8y}=\frac{315}{4} \text{for } y\ne 0$$