The bottom number/expression (denominator) need to be the same to enable direct addition.
Multiply by 1 and you do not change the value. Multiply by 1 but in the form of 1=(x+5)/(x+5) 1=x+5x+5 you do not change the value but you do change the way it looks.
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Multiply 1/(x+3)1x+3 by 1 but in the form of 1=(x+5)/(x+5)1=x+5x+5
Giving color(brown)(1/(x+3)xx(x+5)/(x+5) = (x+5)/((x+3)(x+5)))1x+3×x+5x+5=x+5(x+3)(x+5)
Multiply 1/(x+5)1x+5 by 1 but in the form of 1=(x+3)/(x+3)1=x+3x+3
Giving color(brown)(1/(x+5)xx(x+3)/(x+3) = (x+3)/((x+3)(x+5)))1x+5×x+3x+3=x+3(x+3)(x+5)
color(blue)("Putting it all together")Putting it all together
" "(x+5)/((x+3)(x+5)) + (x+3)/((x+3)(x+5))=1 x+5(x+3)(x+5)+x+3(x+3)(x+5)=1
" "(2x+8)/((x+3)(x+5))=1 2x+8(x+3)(x+5)=1
Multiply both sides by (x+3)(x+5)(x+3)(x+5) giving
" "(2x+8)xx(cancel((x+3)(x+5)))/(cancel((x+3)(x+5)))=1xx(x+3)(x+5)
" "2x+8=x^2+8x+15
" "x^2+6x+7=0
Use the formula to solve for x
I will let you do that
y=ax^2+bx+c" " where " "x=(-b+-sqrt(b^2-4ac))/(2a)
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