Question

What is the simplified form of x plus 4 over x squared minus 3x minus 10 ⋅ x minus 3 over x squared plus x minus 12 ?

Answer 1

I got
x^2-3x-10, or
(x-5)(x+2)

Answer 2

The simplified for of given expression is $\bold{\frac{1}{x^2-3x-10}}$

What is expression?

"It is a mathematical statement which consists of numbers, variables and some mathematical operations."

What is quadratic expression?

"It is a polynomial expression with degree 2."

For given question,

We have been given an expression $\frac{x+4}{x^2-3x-10}\times \frac{x-3}{x^2+x-12}$

We need to find the simplified form of given expression.

First we solve the quadratic expressions at the denominators.

Consider quadratic expression $x^2-3x-10$

$\Rightarrow x^2-3x-10\\\\= x^2-5x+2x-10\\\\=x(x-5)+2(x-5)\\\\=(x-5)(x+2)$

So, the expression $\frac{x+4}{x^2-3x-10}$ would be,

$\frac{x+4}{x^2-3x-10}=\frac{x+4}{(x-5)(x+2)}$

Now consider quadratic expression $x^2+x-12$

$\Rightarrow x^2+x-12\\\\= x^2+4x-3x-12\\\\=x(x+4)-3(x+4)\\\\=(x+4)(x-3)$

So, the expression $\frac{x-3}{x^2+x-12}$ would be,

$\frac{x-3}{x^2+x-12} =\frac{x-3}{(x+4)(x-3)}$

The given expression would be,

$\frac{x+4}{x^2-3x-10}\times \frac{x-3}{x^2+x-12}\\\\=\frac{x+4}{(x-5)(x+2)}\times \frac{x-3}{(x+4)(x-3)}\\\\=\frac{1}{(x-5)(x+2)}\\\\ =\frac{1}{x^2-3x-10}$

Therefore, the simplified for of given expression is $\bold{\frac{1}{x^2-3x-10}}$

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