Algebraic Fractions

Fully simplify the following expression

Express $\displaystyle \large\frac{7}{x+5}-\frac{3}{x}\normalsize$    $\displaystyle \small x\neq-5,\ x\neq0$
as a single fraction in its simplest form.

Express $\displaystyle \large\frac{5t}{s} \normalsize \div \large \frac{t}{2s^2}$
in its simplest form.

Express $\displaystyle \frac{3}{x-2}+\frac{5}{x+1}$, $\displaystyle x\ne2$, $\displaystyle x\ne-1$ as a single fraction in its simplest form.

Express $\displaystyle \large\frac{4}{x+2}-\frac{3}{x-4}\small,\:\: x\neq-2,\ x\neq 4\:\:$
as a single fraction in its simplest form.

Simplify $\displaystyle \large\frac{x^2-4x}{x^2+x-20}\small.$

Express $\displaystyle \frac{3}{a^{2}}-\frac{2}{a}$, $\displaystyle a\ne0$, as a single fraction in its simplest form.

(a)  Factorise $\displaystyle 4x^{2}-25.$

(b)  Hence simplify $\displaystyle \frac{4x^{2}-25}{2x^{2}-x-10}.$

Express $\displaystyle \frac{n}{n^{2}-4}\div\frac{3}{n-2}$, $\displaystyle n\ne-2, n\ne2$ as a single fraction in its simplest form.

Express $\displaystyle \frac{4}{x-2}-\frac{3}{x+5}$, $\displaystyle x\ne2, x\ne-5$, as a single fraction in its simplest form.

Simplify $\displaystyle \frac{2ab+6a}{b^{2}-9}$.

Express $\displaystyle \large\frac{7}{x-3}-\frac{2}{x}\normalsize\:\:\:\:\small x\neq3,\ x\neq0\:\:$
as a single fraction in its simplest form.

Simplify $\displaystyle \large\frac{x^2-16}{x^2+x-20}.$

(a)  Factorise $\displaystyle y^2-6y.$
(b)  Hence simplify $\displaystyle \frac{y^2-6y}{y^2-3y-18}.$

Express $\displaystyle \frac{2}{x+5} + \frac{3}{x-4}$, $\displaystyle x \neq -5, x \neq 4$ as a single fraction in its simplest form.

Express $\displaystyle \frac{5}{x-1}-\frac{4}{x},$ $\displaystyle x \neq 1, x \neq 0$ as a single fraction in its simplest form.