Question 85434
Question:


{{{ (x/(5x+10)) / ((x-3)/(x+2))}}} = {{{7/5}}}



Take the reciprocal of the denomiator in the left hand side and multiply with the numerator.....



{{{ (x/(5x+10)) * ((x+2)/(x-3))}}} = {{{7/5}}}



==> {{{ (x/(5(x+2))) * ((x+2)/(x-3))}}} = {{{7/5}}}




Here (x+2) is common in both the numerator and denominator...so they will get cancelled.....



==> {{{ (x/5) * (1/(x-3))}}} = {{{7/5}}}





==> {{{ (x/5(x-3))}}} = {{{ 7/5}}}




Here 5 is common in the denominator of both sides of the expression, so they will get cancelled......


==> {{{ (x/(x-3))}}} = {{{ 7/1}}}





Now multiply the whole expression by 1* (x-3)...that is the whole terms in the denominators (both sides)



==> {{{ ((x*(x-3))/(x-3))}}} = {{{ (7*(x-3))/1}}}




==> {{{ ((x)/1)}}} = {{{ (7*(x-3))/1}}}



==> x = 7(x-3)



==> x = 7x -21



add 21 to both sides of the expression.....




==> x + 21 = 7x 


subtract x from both sides of the expression.....



==> x + 21 - x = 7x - x



==> 21 = 6x



Divide both sides of the expression by 6....



==> {{{ 21/6 }}} = x



So solution is  x = {{{21/6}}}



Hope you found the explanation useful....



Regards,



Praseena.