Question

x-3÷4x^4-8x^3-18x^2+17x+3​

Answer 1

Answer:

The simplication of x-3÷4x^4-8x^3-18x^2+17x+3 is $\frac{1}{\left(4 x^{3}+4 x^{2}-6 x-1\right)}$

Solution:

$\text { Given, expression is }(x-3) \div\left(4 x^{4}-8 x^{3}-18 x^{2}+17 x+3\right)$

Now we have to simplify the given expression,

For that, we have to factorize the denominator.

$\text { So, } 4 x^{4}-8 x^{3}-18 x^{2}+17 x+3$

$\Rightarrow 4 x^{4}+\left(-12 x^{3}+4 x^{3}\right)+\left(-12 x^{2}-6 x^{2}\right)+(18 x-x)+3$

By grouping terms we get,

$\rightarrow\left(4 x^{4}-12 x^{3}\right)+\left(4 x^{3}-12 x^{2}\right)-\left(6 x^{2}-18 x\right)-(x-3)$

By taking the common terms,

$\begin{array}{l}{\rightarrow 4 x^{3}(x-3)+4 x^{2}(x-3)-6 x(x-3)-(x-3)} \\\\ {\rightarrow(x-3)\left(4 x^{3}+4 x^{2}-6 x-1\right)}\end{array}$

$\begin{array}{l}{\text { Now, }(x-3) \div\left(4 x^{4}-8 x^{3}-18 x^{2}+17 x+3\right) \rightarrow \frac{x-3}{\left(4 x^{4}-8 x^{3}-18 x^{2}+17 x+3\right)}} \\\\ {\quad \rightarrow \frac{x-3}{(x-3)\left(4 x^{3}+4 x^{2}-6 x-1\right)}} \\\\ {\quad \rightarrow \frac{1}{\left(4 x^{3}+4 x^{2}-6 x-1\right)}}\end{array}$

Hence, the simplified expression is  $\frac{1}{\left(4 x^{3}+4 x^{2}-6 x-1\right)}$