Question

please give answer fast​

Answer 1

Step-by-step explanation:

The given equation is |x+y/x-y| is not equal to |x-y/x+y|

x =9/5 and y = 5/3

putting the value in the above equation

-9/5+5/3 /-9/5- 5/3. = -27+25/15 / -27-25/15 here 15 of denominator will get cut

-2/-52 = 2/52 for LHS

for rhs

the answer will be 52/2 as LHS is just a reciprocal of RHS

so we can say that LHS is not equal to RHS

hence proved

hope it will be helpful!!!!!!

Answer 2

GIVEN :-

$\\ \red\bigstar \displaystyle \tt \: \bigg | \dfrac{x + y}{x - y} \bigg | \neq \bigg| \frac{x - y}{x + y} \bigg|$

TO PROVE :-

$\\ \red\bigstar \displaystyle \tt \: \bigg | \dfrac{x + y}{x - y} \bigg | \neq \bigg| \frac{x - y}{x + y} \bigg|$

SOLUTION :-

$\\ \red\bigstar \displaystyle \tt \: \bigg | \dfrac{x + y}{x - y} \bigg | \neq \bigg| \frac{x - y}{x + y} \bigg|$

$\implies \: \displaystyle \tt \: \Bigg| \dfrac{ \dfrac{ - 9}{5} + \dfrac{5}{3} }{ \dfrac{ - 9}{5} - \dfrac{5}{3} } \Bigg| \neq \: \Bigg| \dfrac{ \dfrac{ - 9}{5} - \dfrac{5}{3} }{ \dfrac{ - 9}{5} + \dfrac{5}{3} } \Bigg|$

$\implies \: \displaystyle \tt \: \Bigg | \dfrac{ \dfrac{ - 27 +25 }{15} }{ \dfrac{ - 27 - 25}{15} } \bigg | \neq \: \Bigg | \dfrac{ \dfrac{ - 27 - 25 }{15} }{ \dfrac{ - 27 + 25}{15} } \Bigg |$

$\implies \: \displaystyle \tt \: \Bigg | \dfrac{ \dfrac{ - 2}{15} }{ \dfrac{ - 52}{15} } \Bigg | \neq\Bigg | \dfrac{ \dfrac{ - 52}{15} }{ \dfrac{ - 2}{15} } \Bigg |$

$\implies \: \displaystyle \tt \: \bigg | \dfrac{ - 2}{15} \times \dfrac{ - 15}{52} \bigg | \neq \: \bigg | \dfrac{ - 52}{15} \times \dfrac{ - 15}{2} \bigg |$

$\implies \: \displaystyle \tt \: \bigg | \dfrac{ 2}{ \cancel{15}} \times \dfrac{ \cancel{15}}{52} \bigg | \neq \: \bigg | \dfrac{ 52}{ \cancel{15}} \times \dfrac{ \cancel{15}}{2} \bigg |$

$\implies \: \displaystyle \tt \: \bigg | \dfrac{2}{52} \bigg | \neq \: \bigg | \dfrac{52}{2} \bigg |$

$\implies \: \displaystyle \tt \: \bigg | \frac{1}{26} \bigg | \neq \: \bigg | \frac{26}{1} \bigg |$

$\implies \: \displaystyle \tt \: \dfrac{1}{26} \neq \: 26$

$\therefore \displaystyle \tt \: \bigg | \dfrac{x + y}{x - y} \bigg | \neq \bigg| \frac{x - y}{x + y} \bigg|$

HENCE PROVED ✅