Question 35312
{{{5/(7(x+5)) +1/(42(x+3)) }}}


Your problem was that you did not find the Lowest Common Denominator.  Notice that 7 divides evenly into 42, so the LCD = {{{42(x+5)(x+3) }}}


Now, multiply the first fraction by 6(x+3) and the second fraction by (x+5):


{{{(5/(7(x+5)))*((6(x+3))/(6(x+3))) +(1/(42(x+3)))*((x+5)/(x+5)) }}}


Now, the LCD is 42(x+3)(x+5), and that becomes the denominator of the fraction.  The numerator of the fraction becomes the sum of the numerators.
{{{ (30(x+3) + (x+5) ) /(42(x+3)(x+5)) }}}


NOW DON'T DIVIDE ANY OF THESE OUT!!  They look like factors, but they are NOT factors!!  Multiply out the numerators.
{{{ (30(x+3) + (x+5) ) /(42(x+3)(x+5)) }}}
{{{ (30x+90 + x+5)/(42(x+3)(x+5)) }}}
{{{ (31x+95 )/(42(x+3)(x+5)) }}}


R^2 at SCC