#936 · Algebra · Linear equations

Fractional Sum with Cubes

If $\frac{x}{a} = \frac{y}{b} = \frac{z}{c}$ , shew that $\frac{x ^{3} + a ^{3}}{x ^{2} + a ^{2}} + \frac{y ^{3} + b ^{3}}{y ^{2} + b ^{2}} + \frac{z ^{3} + c ^{3}}{z ^{2} + c ^{2}} = \frac{( x + y + z ) ^{3} + ( a + b + c ) ^{3}}{( x + y + z ) ^{2} + ( a + b + c ) ^{2}}$ .

~10 minProof · checked by AIratiosubstitutionalgebraic simplification

H. S. Hall & S. R. Knight, Higher Algebra (1891) · Ch. I. Ratio, Examples I, No. 12

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