Math, asked by abusalman847, 6 months ago

25xsquareysquarez(x square -14 x-51) divided by 5xy(x-17)(x square-9)

Answers

Answered by blossom40cherry

Step-by-step explanation:

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Answered by brokendreams

Step-by-step explanation:

Given : A fraction $\frac{25x^{2} y^2z(x^{2} -14x-51)}{5xy(x-17)(x^{2} -9)}$

To find : The simplified value of given fraction.

Formula used : We use algebraic identity,

$a^2-b^2=(a-b)(a+b)$

We have

$\frac{25x^{2} y^2z(x^{2} -14x-51)}{5xy(x-17)(x^{2} -9)}$

To solve this question let's take numerator and denominator separately such as,

Numerator $=25x^2y^2z(x^{2} -14x-51)$

Denominator $=5xy(x-17)(x^2-9)$

Taking numerator first ;

Numerator $=25x^2y^2z(x^{2} -14x-51)$

we have a quadratic equation inside the bracket of numerator,

⇒ $x^2-14x-51=0$

Solving the expression by splitting the middle term (finding factors of $-51$ such that they give up to $-14$ )

⇒ $x^{2} -17x+3x-51=0$

⇒ $x(x-17)+3(x-17)$

⇒ $(x+3)(x-17)$

We get the factors of equation as $(x+3)(x-17)$ .

So the numerator is $25x^2y^2z(x-17)(x+3)$ .

Taking denominator;

Denominator $=5xy(x-17)(x^2-9)$

we can write $(x^{2} -9)$ by using algebraic identity where a and b are,

$a=x$ and $b=3$

⇒ $(x^2-9)=(x-3)(x+3)$

Now the denominator is $5xy(x-17)(x-3)(x+3)$

Now the fraction by using new numerator and denominator is,

⇒ $\frac{25x^2y^2z(x-17)(x+3)}{5xy(x-17)(x-3)(x+3)}$

cancelling the same terms from numerator and denominator,

⇒ $\frac{5xyz}{(x-3)}$

So we get the answer as $\frac{5xyz}{(x-3)}$ .

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