Mymathware Shafii's math academy

Evaluate $x$ in the equation $\frac{x^2-10}{x-3}+\frac{1}{x-3}=\frac{1}{5}$ Solution First we need to find the Lowest Common Multiple (LCM) of the left hand …

Let $f:A\rightarrow{A}$ with $f(x)=\frac{x+2}{x-3}$ for $A=\mathbb{R}/\{1,3\}$ Show that $f$ is a one-to-one function. Proof: we are given $f:A\rightarrow{A}…

Let $a,b\in\mathbb{R}$. Prove th inequality $\frac{a}{b}+\frac{b}{a}\geq{2}$ Proof We are given $\frac{a}{b}+\frac{b}{a}\geq{2}$, . Let $(a-b)^2\geq{0}$ so t…

The product of the third and the sixth terms of an arithmetic sequence is $406$. The ninth term of the sequence divided by the fourth term gives a quotient of $2$ and a …

Find the sum of all natural numbers between $1$ and $1000$ that are not divisible by $13$. Let $S$ be the unknown sum and $M$ multiples of $13$ less than $1000$, then $S…

Solve the equation $2\cosh{2x}+10\sinh{2x}=5$ ................. 🆔 This is a hyperbolic trigonometric function equation, in order to solve the given equation, we must re…