How Do You Solve for x2 in the Equation a1b1/x1 = a2b2/x2?

[iamjon.smith]

Homework Statement

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a₁b₁/x₁= a₂b₂/x₂solve for x₂

Homework Equations

no relevant questions apply, this is a stand alone review question

The Attempt at a Solution

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multiply times reciprocal to get rid of denominator on left

(x₁) (a₁b₁/x₁)= (a₂b₂/x₂)(x₁)

a₁b₁ = (a₂b₂x₁/x₂)

multiply times reciprocal to get rid of denominator on right

(x₂) a₁b₁/x₁= a₂b₂x₁/x₂ (x₂)

a₁b₁x₂ = a₂b₂x₁

divide by a₁b₁ to get x₂ alone

a₁b₁x₂/a₁b₁ = a₂a₂x₁/(a₁b₁)

x₂ = a₂b₂x₁/(a₁b₁) I know I have missed something, but this is my best attempt at solving this problem. Could someone please review and help me figure out what I missed?

 

[Ray Vickson]

You have not missed anything; your answer is correct (provided that you never divide by zero anywhere, so provided that all x's a's and b's are nonzero). Your argument is very long-winded, though, and can be shortened into two lines:
\frac{a_1 b_1}{x_1} = \frac{a_2 b_2}{x_2}\, ,\\<br /> \text{so }\; \frac{x_1}{a_1 b_1} = \frac{x_2}{a_2 b_2} \, ,\\<br /> \text{so }\; x_2 = \frac{x_1}{a_1 b_1} a_2 b_2 = \frac{a_2 b_2 x_1}{a_1 b_1}