Question
Simplify.
$$\frac{2}{y+1}-\frac{3}{y}$$
Give your answer as a single fraction in its simplest form.
▶️Answer/Explanation
$\frac{-y – 3}{y(y + 1)} \, \text{or} \, \frac{-y – 3}{y^2 + y} \, \text{or} \, \frac{-y + 3}{y(y + 1)} \\
\text{or} \, \frac{-y + 3}{y^2 + y} \, \text{(final answer)}$
$
\frac{2}{y+1} – \frac{3}{y}
$
$
= \frac{2 \cdot y}{y(y+1)} – \frac{3(y+1)}{y(y+1)}
$
$
= \frac{2y – (3y + 3)}{y(y+1)}
$
$
= \frac{2y – 3y – 3}{y(y+1)}
$
$
= \frac{-y – 3}{y(y+1)}
$
Question
Simplify.
$$7x-8y-x-y$$
▶️Answer/Explanation
$6x-9y$ or $3(2x-3y)$ final answer
$
7x – 8y – x – y
$
For the \(x\) terms
$
7x – x = 6x
$
For the \(y\) terms
$
-8y – y = -9y
$
$
6x – 9y
$
Question
Factorise completely.
$( \mathbf{a} )$ $12m^2- 75t^2$
$( \mathbf{b} )$ $xy+ 15+ 3y+ 5x$
▶️Answer/Explanation
(a) $3(2m+5t)(2m-5t)$ final answer (b) $(x+3)(y+5)$ final answer
(a)
$
12m^2 – 75t^2
$
The coefficients: 12 and 75.
The greatest common factor (GCF) is 3.
$
12m^2 – 75t^2 = 3(4m^2 – 25t^2)
$
The expression inside the brackets is a difference of squares.
$
a^2 – b^2 = (a – b)(a + b)
$
\( 4m^2 = (2m)^2 \)
\( 25t^2 = (5t)^2 \)
$
= 3(2m – 5t)(2m + 5t)
$
(b)
$
xy + 15 + 3y + 5x
$
$
= (xy + 3y) + (5x + 15)
$
$
= y(x + 3)
$
$
= 5(x + 3)
$
(x + 3) is common in both terms
$
= (x + 3)(y + 5)
$
Question
Simplify the expression.
\(\left ( a^{\frac{1}{2}}- b^{\frac{1}{2}}\right )\left ( a^{\frac{1}{2}}+ b^{\frac{1}{2}}\right )\)
Answer/Explanation
Ans: a(1) – b(1) www cao
Question
Simplify.
\(\frac{x^{2}-16}{x^{2}-3x-4}\)
Answer/Explanation
Ans: \(\frac{x+4}{x+1}\) final answer
Question
Factorise completely.
15p2 + 24pt
Answer/Explanation
Ans: 3p(5p + 8t) final answer