Question

What is the simplified form of the quantity of x plus 4, all over the quantity of 7 − the quantity of x plus 3, all over the quantity of x plus 5?

Answer 1

`(x + 4)/(7) -(x + 3)/(x + 5) =((x + 4)(x + 5))/(7(x + 5)) -(7(x + 3))/(7(x + 5)) =(x(x + 5) + 4(x + 5))/(7(x) + 7(5)) - (7(x) + 7(3))/(7(x) + 7(5)) =(x(x) + x(5) + 4(x) + 4(5))/(7x + 35) - (7x + 21)/(7x + 35) =(x^(2) + 5x + 4x + 20)/(7x + 35) -(7x + 21)/(7x + 35) =(x^(2) + 9x + 20)/(7x + 35) - (7x + 21)/(7x + 35) =((x^(2) + 9x + 20) - (7x + 21))/(7x + 35) =(x^(2) + (9x - 7x) + (20 - 21))/(7x + 35) =(x^(2) + 2x -1)/(7x + 35)`