JAMB 2018 Mathematics · Question 29

If xa+1\frac{x}{a + 1} + yb\frac{y}{b} = 1. Make y the subject of the relation.

Options

  1. A.b(a+1−x)a+1\frac{b(a + 1 - x)}{a + 1}
  2. B.a+1b(a−x+1)\frac{a + 1}{b(a - x + 1)}
  3. C.a(b−x+1)b+1\frac{a(b - x + 1)}{b + 1}
  4. D.ba(b−x+1)\frac{b}{a(b - x + 1)}

Answer: A. b(a+1−x)a+1\frac{b(a + 1 - x)}{a + 1}

Explanation written with AI and checked against the answer key

To make yy the subject of the formula, we need to isolate yy on one side of the equation. Let’s break it down step-by-step.

1. Analyze the equation

The given equation is:

xa+1+yb=1\frac{x}{a + 1} + \frac{y}{b} = 1
2. Explain the concept

To isolate yy, we follow the order of operations in reverse:

  • First, move the term not containing yy to the other side of the equation.
  • Second, multiply by the denominator of the yy term to clear the fraction.
3. Step-by-step solution

Step 1: Subtract xa+1\frac{x}{a + 1} from both sides

yb=1−xa+1\frac{y}{b} = 1 - \frac{x}{a + 1}

Step 2: Simplify the right side by finding a common denominator The common denominator is (a+1)(a + 1):

yb=a+1a+1−xa+1\frac{y}{b} = \frac{a + 1}{a + 1} - \frac{x}{a + 1}
yb=a+1−xa+1\frac{y}{b} = \frac{a + 1 - x}{a + 1}

Step 3: Solve for yy by multiplying both sides by bb

y=b×(a+1−xa+1)y = b \times \left( \frac{a + 1 - x}{a + 1} \right)
y=b(a+1−x)a+1y = \frac{b(a + 1 - x)}{a + 1}
4. Identify the answer

Comparing our result with the given options, it matches option A.

5. Exam Tip

When dealing with algebraic fractions in JAMB, always look for the "common denominator" first. If you have a constant (like 11) and a fraction, you can always write the constant as a fraction with the same denominator (e.g., 1=a+1a+11 = \frac{a+1}{a+1}) to make subtraction much easier and avoid errors with signs.

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