Question

4Xsquare -11x+6 upon 16Xsqyare -9

Answer 1

x-2/4x+3 is the answer

Answer 2

Step-by-step explanation:

Given : A fraction $\frac{4x^{2} -11x+6}{16x^{2} -9}$

To find : The value of given fraction

Formula used : An algebraic identity

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

• Calculation for fraction

We have fraction

$\frac{4x^{2} -11x+6}{16x^{2} -9}$

We can see there is a quadratic equation in numerator and in denominator there is also equation so to solve them we can take numerator and denominator separately as,

Numerator $=4x^{2} -11x+6$

Denominator $=16x^{2} -9$

Now taking numerator first,

Numerator $=4x^{2} -11x+6$

this is a quadratic equation so we can equate it by zero.

⇒  $4x^{2} -11x+6=0$

Solving the expression by splitting the middle term (finding factors of 24 such that they add up to -11 )

⇒  $4x^{2} -8x-3x+6=0$

⇒  $4x(x-2)-3(x-2)=0$

⇒  $(4x-3)(x-2)$

now our numerator is $(4x-3)(x-2)$.

Taking denominator,

Denominator $=16x^{2} -9$

writing denominator as the algebraic identity, where

$a=4x$       and      $b=3$

so we can write denominator as,

⇒  $16x^{2} -9=(4x-3)(4x+3)$

so our new denominator is $(4x-3)(4x+3)$

now the fraction is,

⇒  $\frac{(4x-3)(x-2)}{(4x-3)(4x+3)}$

cancelling $(4x-3)$ from both numerator and denominator

⇒  $\frac{(x-2)}{(4x+3)}$

so the answer we get as $\frac{(x-2)}{(4x+3)}$.