Question

efectuati:
$\frac{a}{a - b} - \frac{ b}{a + b}$
​

Answer 1

= a(a+b)/(a-b)(a+b) - b(a-b)/(a-b)(a+b) = (a²+ab-ab+b²)/(a-b)(a+b) = (a²+b²)/(a²-b²)

Answer 2

Răspuns: $\color{blueviolet}\Large\boxed{ \bf \dfrac{a^{2} +b^{2}}{a^{2} -b^{2}} }$

Explicație pas cu pas:

$\large \bf \!{^{^{^{^{^{^{\displaystyle (a+b)\Big)}}}}}}}\!\!\!\!\dfrac{a}{a-b} -\!{^{^{^{^{^{^{\displaystyle (a-b)\Big)}}}}}}}\!\!\!\!\dfrac{b}{a+b} =$

$\it~~~$

$\large \bf\dfrac{a\cdot (a+b)}{(a-b)\cdot(a+b)} -\dfrac{b\cdot(a-b)}{(a-b)\cdot(a+b)} =$

$\it~~$

$\large \bf\dfrac{a^{2} +ab - (ab -b^{2})}{(a-b)\cdot(a+b)} =\dfrac{a^{2} +ab - ab+b^{2}}{(a-b)\cdot(a+b)} =$

$\it~~$

$\color{red}\Large\boxed{ \bf \dfrac{a^{2} +b^{2}}{a^{2} -b^{2}} }$

==pav38==