If a and b are two rational numbers prove that a+b ,a-b , ab are rational numbers. If b is not equal to 0 show that a/b is also a rational number

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Solution

$a space equals space p over q space space comma space space b space equals r over s a plus b space equals space p over q space plus space r over s space equals space fraction numerator p cross times s space plus space q cross times r over denominator q cross times s end fraction space left parenthesis f r a c t i o n a l space a d d i t i o n right parenthesis a minus b space equals space p over q space minus space r over s space equals space fraction numerator p cross times s space minus space q cross times r over denominator q cross times s end fraction space left parenthesis f r a c t i o n a l space s u b t r a c t i o n right parenthesis p cross times s space plus-or-minus space q cross times r space i s space p r o d u c t space o f space t w o space n o n space z e r o space i n t e g e r s space comma space s o space i t space w o u l d space b e space a l s o space i n t e g e r s q cross times s space i s space t h e space p r o d u c t space o f space t w o space n o n space z e r p space i n t e g r s space. s o space i t space i s space a l s o space n o n space z e r o space n u m b e r. s o space t h e space a b o v e space c o n d i t i o n space a c c e p t space t h e space c o n d i t i o n space o f space r a t i o n a l space n u m b e r s$

like if satisfied

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Similar questions

If a, b, c are rational numbers such that a² + b² + c² − ab − bc − ca = 0, prove that a = b = c.

(a - b + c) x^{2} + 2 (a - b) x + (a - b - c) = 0

if b is not equal to 0 how can we showthat a by b is a rational number

\frac{a}{b}

\frac{c}{d}

\frac{a}{b}

\frac{c}{d}

\frac{a}{b} a n d \frac{c}{d}

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