<span> 2.1 </span> Adding a fraction to a whole
Rewrite the whole as a fraction using <span> x </span> as the denominator :
<span>Equivalent fraction : </span>The fraction thus generated looks different but has the same value as the whole
<span>Common denominator : </span>The equivalent fraction and the other fraction involved in the calculation share the same denominator
<span> 2.2 </span> Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
<span> 3.1 </span> Adding a whole to a fraction
Rewrite the whole as a fraction using <span> x </span> as the denominator :
<span> 4.1 </span> Pull out like factors :
<span> 9x2 + 3</span> = <span> 3 • (3x2 + 1)</span>
<span> 4.2 </span> Find roots (zeroes) of : <span> F(x) = 3x2 + 1</span>
Polynomial Roots Calculator is a set of methods aimed at finding values of x for which F(x)=0
Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers x which can be expressed as the quotient of two integers
The Rational Root Theorem states that if a polynomial zeroes for a rational number P/Q then P is a factor of the Trailing Constant and Q is a factor of the Leading Coefficient
In this case, the Leading Coefficient is 3 and the Trailing Constant is <span> 1.
</span>The factor(s) are:
of the Leading Coefficient : <span> 1,3
</span>of the Trailing Constant : <span> 1
</span>Let us test ....
Polynomial Roots Calculator found no rational roots
<span> 4.3 </span> Adding up the two equivalent fractions
<span> 5.1 </span> Subtracting a fraction from a whole
Rewrite the whole as a fraction using <span> x </span> as the denominator :
<span> 5.2 </span> Factoring <span> 9x2 + 4x + 3</span>
The first term is, <span> <span>9x2</span> </span> its coefficient is <span> 9 </span>.
The middle term is, <span> +4x </span> its coefficient is <span> 4 </span>.
The last term, "the constant", is <span> +3 </span>
Step-1 : Multiply the coefficient of the first term by the constant <span> <span> 9</span> • 3 = 27</span>
Step-2 : Find two factors of 27 whose sum equals the coefficient of the middle term, which is <span> 4 </span>.
Observation : No two such factors can be found !!
Conclusion : Trinomial can not be factored
<span> 5.3 </span> Adding up the two equivalent fractions
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the <span>denominator, </span>Tiger multiplys both sides of the equation by the denominator.
Here's how:
Now, on the left hand side, the <span> x </span> cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
<span> px2-9x2-4x-3</span> = 0
<span> 6.2 </span> Solve <span> <span>px2-9x2-4x-3</span> </span> = 0
In this type of equations, having more than one variable (unknown), you have to specify for which variable you want the equation solved.