# Cross Multiplication in a Proportion [closed]

Solve for $$h$$:

$$\frac{h+z}{h} = \frac{a}{b}$$

I'm not sure how to simplify this with cross multiplication.

## closed as off-topic by KReiser, José Carlos Santos, Namaste, Key Flex, Deepesh MeenaSep 28 '18 at 1:38

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – KReiser, José Carlos Santos, Namaste, Key Flex, Deepesh Meena
If this question can be reworded to fit the rules in the help center, please edit the question.

• Is the left side $h + \frac{z}{h}$ or $\frac{h+z}{h}$? – Sean Roberson Sep 27 '18 at 21:33
• $\frac {h+z}{h} = \frac ab$ or $h + \frac {z}{h} = \frac ab$? Formatting is important. – Doug M Sep 27 '18 at 21:36
• (h+z)/h = a/b sorry about that – Katelyn Sep 27 '18 at 21:42
• Using MathJax could avoid confusion like this. – KM101 Sep 27 '18 at 22:29

$$\frac{h+z}{h} = \frac{a}{b}$$
$$\implies b(h+z) = ah$$
$$bh+bz = ah \implies bz = ah-bh \implies bz = (a-b)h \implies h = \frac{bz}{a-b}$$
Multiply both sides of the equation by $$h$$ and you get: $$\\h^2-\frac{a}{b}h+z=0$$ This should be easy to solve as it's just a quadratic.
$$\frac{h^2}{h}+\frac{z}{h} = \frac{a}{b}$$ $$\frac{h^2+z}{h} = \frac{a}{b}$$ $$h^2+z = \frac{a}{b}h$$ $$h^2-\frac{a}{b}h+z=0$$ Using the quadratic formula, we can get $$h = \frac{\frac{a}{b}\pm\sqrt{\left(\frac{a}{b}\right)^2-4z}}{2}$$