Helpful hints

Let us consider y = A .                    (1)
                            B + x

Hint 1. A common mistake that people make when handling fractions is that they can simply split the right hand side of the fraction. They can't.
               y does not = A + A          (2)
                                   B     x
The right hand side of equations (1) and (2) are not both equal.

If you are in any doubt, try substituting in numbers for each of the letters.
For example, let x = 2, A = 2 and B = 3
For equation (1), y = 2/(3+2) = ²/₅
For equation (2), y = 2/3 + 2/2 = 1 ²/₃

Hint 2. Remember what brackets mean in terms of algebra. They are telling you the order that you must carry out the functions of an equation. You carry out the function inside the bracket first. 2/(3+2) means that you add 3 and 2 together, and then divide 2 by this sum.

2/(3+2) = ²/₅ and not 2/3 + 2 = 2²/₃.
This may seem obvious, but under pressure many of your contemporaries seem to forget.

Hint 3. y = A + A       (equation (2))         is not = A+A
                 B      x                                                 B+x

In order to convert equation (2) into one fraction, you have to carry out the following algebra:

A + A = A(x) + A(B)
B     x      Bx        Bx

You can then amalgamate the two fractions = A(x) + B(A)    because they have a common
                                                                             Bx
denominator.

Again, if you are having trouble following this in terms of algebra, go back to substituting numbers for each of the letters. If we consider how we worked out the value of equation (2) using x = 2, A = 2 and B = 3.
y = 2 + 2            Now consider how we would work this out "long hand".
      3    2
Get both fractions with one common denominator (it is obvious with numbers to equal 6)
Ie y = (2x2) + (2x3) = 4 + 6 = 10 = 1⁴/₆ = 1 ²/₃
          (2x3)    (3x2)   6     6     6

Answers
 

Explanation

Q 70     You can't split the lower half of the fraction like that.
Q 71     Answers 2 and 4 can't both be right. Answer 4 is in fact wrong.
Q 72     If x = - B, the bottom half of the fraction = 0, meaning y = infinity.
Q 73     Following on from Q 72, answer 5 in this question is actually correct.
If x = -Q, the bottom half of the fraction = Q+-Q = 0. (P × -Q)/0 = minus infinity. Answer 4 is incorrect. If x = 0, P × x = 0, so y = 0, not P/Q.
Q 74     When y = 0, x = -c/m. Not x = c/m.
Q 75     y is not inversely proportional to x. For this to be true, y would get smaller for increasing values of x, i.e. the gradient would be smaller than 1. The gradient of this line is 2.
Q 76     The gradient of the line is - 3.
Q 77     When y = 0, x = - 1/2 min.
Q 78     The gradient of the line is - 0.2. Thus answer 4 is incorrect.
Q 79     The gradient of the line is - 0.2. Thus answer 1 is incorrect.
Q 80     When x = 3, y = 1.49 (not 1.4).
Q 81     Gradient = y/x. Both units contain ml^-1, which will cancel each other out.
Q 82     Gradient = y/x. Both units contain mmol.l^-1, which will cancel each other out.
Q 83     Log₁₀(a + b) does not equal log₁₀a + log₁₀b.  Log(a x b) = log₁₀a + log₁₀b