Question-189792

Question Number 189792 by normans last updated on 21/Mar/23

Answered by HeferH last updated on 22/Mar/23

Commented by HeferH last updated on 22/Mar/23

(a/(5−a)) = ((9−a)/a); a^2 =5(9−a)−a(9−a) a^2 = 45−5a−9a+a^2 a = ((45)/(14)) ∗ (9/a) = ((m+n)/n); (x/a) = ((p+q)/q) ∗ (m/n) = (q/p) 9 ∙ ((14)/(45)) = (m/n) + 1 ((14)/5)−1=(m/n) ∗ (n/m) = (5/9) = (p/q) x = ((p/q) +1)((45)/(14)) x = ((14)/9) ∙((45)/(14)) = 5

$$\frac{\mathrm{a}}{\mathrm{5}−\mathrm{a}}\:=\:\frac{\mathrm{9}−\mathrm{a}}{\mathrm{a}};\:\: \\ $$$$\:\mathrm{a}^{\mathrm{2}} =\mathrm{5}\left(\mathrm{9}−\mathrm{a}\right)−\mathrm{a}\left(\mathrm{9}−\mathrm{a}\right) \\ $$$$\:\mathrm{a}^{\mathrm{2}} =\:\mathrm{45}−\mathrm{5a}−\mathrm{9a}+\mathrm{a}^{\mathrm{2}} \: \\ $$$$\:\mathrm{a}\:=\:\frac{\mathrm{45}}{\mathrm{14}} \\ $$$$\:\ast\:\frac{\mathrm{9}}{\mathrm{a}}\:=\:\frac{\mathrm{m}+\mathrm{n}}{\mathrm{n}};\:\:\:\frac{\mathrm{x}}{\mathrm{a}}\:=\:\frac{\mathrm{p}+\mathrm{q}}{\mathrm{q}} \\ $$$$\:\ast\:\frac{\mathrm{m}}{\mathrm{n}}\:=\:\frac{\mathrm{q}}{\mathrm{p}} \\ $$$$\:\mathrm{9}\:\centerdot\:\frac{\mathrm{14}}{\mathrm{45}}\:=\:\frac{\mathrm{m}}{\mathrm{n}}\:+\:\mathrm{1}\: \\ $$$$\:\frac{\mathrm{14}}{\mathrm{5}}−\mathrm{1}=\frac{\mathrm{m}}{\mathrm{n}} \\ $$$$\:\ast\:\frac{\mathrm{n}}{\mathrm{m}}\:=\:\frac{\mathrm{5}}{\mathrm{9}}\:=\:\frac{\mathrm{p}}{\mathrm{q}} \\ $$$$\:\mathrm{x}\:=\:\left(\frac{\mathrm{p}}{\mathrm{q}}\:+\mathrm{1}\right)\frac{\mathrm{45}}{\mathrm{14}} \\ $$$$\:\mathrm{x}\:=\:\frac{\mathrm{14}}{\mathrm{9}}\:\centerdot\frac{\mathrm{45}}{\mathrm{14}}\:=\:\mathrm{5}\: \\ $$

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