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sim0nz12345 · Feb 24, 2007, 04:41 AM

Hi there
Could you please give me a step by step instruction of the following questions:

Make y the subject in
1/x^2-1/z^2=1/y^2

Thanks

galactus · Feb 24, 2007, 10:51 AM

I assume by 'make y the subject', you mean solve for y?

$\frac{1}{x^{2}}-\frac{1}{z^{2}}=\frac{1}{y^{2}}$

Multiply by $x^{2}y^{2}z^{2}$

$\not{x^{2}}y^{2}z^{2}\cdot\frac{1}{\not{x^{2}}}-x^{2}y^{2}\not{z^{2}}\cdot\frac{1}{\not{z^{2}}}=x^ {2}\not{y^{2}}z^{2}\cdot\frac{1}{{\not{y^{2}}}$

$y^{2}z^{2}-x^{2}y^{2}=x^{2}z^{2}$

Factor out $y^{2}$

$y^{2}(z^{2}-x^{2})=x^{2}z^{2}$

$y^{2}=\frac{x^{2}z^{2}}{z^{2}-x^{2}}$

$y=\sqrt{\frac{x^{2}z^{2}}{z^{2}-x^{2}}}$

$y=\frac{xz}{\sqrt{z^{2}-x^{2}}}$

sim0nz12345 · Feb 24, 2007, 05:27 PM

Oh I'm terribly sorry... Thanks very much for your help I appreciate it.
I'll remember to rate your answers.
Thanks