Difference between revisions of "1955 AHSME Problems/Problem 4"

Revision as of 23:03, 6 July 2018

Problem

The equality $\frac{1}{x-1}=\frac{2}{x-2}$ is satisfied by:

$\textbf{(A)}\ \text{no real values of }x\qquad\textbf{(B)}\ \text{either }x=1\text{ or }x=2\qquad\textbf{(C)}\ \text{only }x=1\\ \textbf{(D)}\ \text{only }x=2\qquad\textbf{(E)}\ \text{only }x=0$

Solution

From the equality, $\frac{1}{x-1}=\frac{2}{x-2}$ , we get ${(x-1)}\times2={(x-2)}\times1$ .

Solving this, we get, ${2x-2}={x-2}$ .

Thus, only {x=0} can satisfy the equation.

Revision as of 23:03, 6 July 2018 (view source) Awesomechoco (talk \| contribs) (→‎Solution) ← Older edit		Revision as of 23:03, 6 July 2018 (view source) Awesomechoco (talk \| contribs) (→‎Solution) Newer edit →
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	Solving this, we get, <math>{2x-2}={x-2}</math>.		Solving this, we get, <math>{2x-2}={x-2}</math>.

−	Thus, only ${x=0} can satisfy the equation.	+	Thus, only {x=0} can satisfy the equation.

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Difference between revisions of "1955 AHSME Problems/Problem 4"

Revision as of 23:03, 6 July 2018

Problem

Solution