#1/(2b + 1) + 1/(b + 1) > 8/15#
Solving the LHS..
#(1 (b + 1) + 1 (2b + 1))/((2b + 1) (b + 1)) > 8/15#
#(b + 1 + 2b + 1)/((2b + 1) (b + 1)) > 8/15#
Collecting like terms
#(b + 2b + 1 + 1 )/((2b + 1) (b + 1)) > 8/15#
#(3b + 2)/((2b + 1) (b + 1)) > 8/15#
Expanding the denominator
#(3b + 2)/(2b^2 + 2b + b + 1) > 8/15#
#(3b + 2)/(2b^2 + 3b + 1) > 8/15#
Cross multiplying
#15(3b + 2) > 8(2b^2 + 3b + 1)#
Expanding..
#45b + 30 > 16b^2 + 24b + 8#
Restructuring the equation.. Note #-># Why am doing this because I don't want any form of confusion to come in.. to make it more simpler to understand..
Also when restructuring equations, the inequality sign changes!
#16b^2 + 24b + 8 < 46b + 30#
Collecting like terms...
#16b^2 + 24b - 46b + 8 - 30 < 0#
#16b^2 - 22b - 22 < 0 -> "Quadratic Equation"#
Should I go further...?!
