Question

Simplify by factorisation method 9-2root3-x^2/3-x^2

Answer 1

The solution is $\frac{x+3\sqrt{3} }{x+\sqrt{3} }$

Explanation:

The expression is $\frac{9-2\sqrt{3} x-x^{2} }{3-x^{2} }$

Simplifying, we have,

$\frac{-(- 9+2\sqrt{3} x+x^{2} )}{-(-3+x^{2} )}$

Dividing we get,

$\frac{- 9+2\sqrt{3} x+x^{2} }{x^{2}-3 }$

Factoring, we get,

$\frac{- 9+3\sqrt{3} x-\sqrt{3} x+x^{2} }{x^{2}-(\sqrt{3})^2 }$

Taking out the common terms,

$\frac{x(x-\sqrt{3} )+3\sqrt{3}( x- \sqrt{3}) }{(x+\sqrt{3})(x-\sqrt{3})}$

Simplifying, we have,

$\frac{(x-\sqrt{3} )(x+3\sqrt{3}) }{(x+\sqrt{3})(x-\sqrt{3})}$

Cancelling the common terms, we get,

$\frac{x+3\sqrt{3} }{x+\sqrt{3} }$

Thus, the solution is $\frac{x+3\sqrt{3} }{x+\sqrt{3} }$

Learn more:

(1) brainly.in/question/1172376

(2) brainly.in/question/3617923