Question Number 104253 by Anindita last updated on 20/Jul/20
$$\mathrm{When}\:{a}\ast{b}=\:\frac{{a}+{b}}{{a}−{b}}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the} \\ $$$$\mathrm{answer}\:\mathrm{of}\:\mathrm{2}\ast\mathrm{3}×\mathrm{9}\ast\mathrm{10}\:? \\ $$
Commented by som(math1967) last updated on 20/Jul/20
$$\frac{\mathrm{2}+\mathrm{3}}{\mathrm{2}−\mathrm{3}}×\frac{\mathrm{9}+\mathrm{10}}{\mathrm{9}−\mathrm{10}}=\frac{\mathrm{5}}{−\mathrm{1}}×\frac{\mathrm{19}}{−\mathrm{1}}=\mathrm{95} \\ $$
Answered by OlafThorendsen last updated on 20/Jul/20
$$\mathrm{2}\ast\mathrm{3}\:=\:\frac{\mathrm{2}+\mathrm{3}}{\mathrm{2}−\mathrm{3}}\:=\:−\mathrm{5} \\ $$$$\mathrm{9}\ast\mathrm{10}\:=\:\frac{\mathrm{9}+\mathrm{10}}{\mathrm{9}−\mathrm{10}}\:=\:−\mathrm{19} \\ $$$$\mathrm{2}\ast\mathrm{3}×\mathrm{9}\ast\mathrm{10}\:=\:\left(−\mathrm{5}\right)×\left(−\mathrm{19}\right)\:=\:\mathrm{95} \\ $$