Subtract. The numerator should be expanded and simplified. The denominator should be either expanded or factored. (4)/(9x^(2)-45 x)-(6x)/(x^(2)-25)=

Question

Subtract. The numerator should be expanded and simplified. The denominator should be either expanded or factored.  (4)/(9x^(2)-45 x)-(6x)/(x^(2)-25)=

Bytelearn · Accepted Answer

Identify Denominator Structure: First, we need to identify the structure of the denominators in both fractions to see if they can be factored. The first denominator is 9x^2 - 45x, which can be factored by taking out the common factor of 9x, resulting in 9x(x - 5). The second denominator is x^2 - 25, which is a difference of squares and can be factored into (x + 5)(x - 5).Factor Denominators: Now that we have factored the denominators, we can rewrite the expression with these factors: (4)/(9x(x - 5)) - (6x)/((x + 5)(x - 5))Rewrite with Factored Denominators: To subtract these fractions, we need a common denominator. The least common denominator (LCD) for these two fractions is 9x(x - 5)(x + 5). We will rewrite each fraction with the LCD as the denominator.Find Common Denominator: The first fraction already has 9x(x - 5) in the denominator, so we only need to multiply the second fraction by 9x/9x to get the LCD in the denominator: (4)/(9x(x - 5)) - (6x * 9x)/((x + 5)(x - 5) * 9x)Simplify Fractions: Now we simplify the second fraction: (4)/(9x(x - 5)) - (54x^2)/((x + 5)(x - 5) * 9x)Combine Like Terms: We can now subtract the fractions since they have the same denominator: (4 - 54x^2)/(9x(x - 5)(x + 5))Factorize Numerator: Next, we expand the numerator to combine like terms: (4 - 54x^2)/(9x(x^2 - 25))Cancel Common Factors: We can simplify the numerator by factoring out a -2 (since 4 is not divisible by 54, but we can take out the negative to make the x^2 term positive): (-2 * (27x^2 - 2))/(9x(x^2 - 25))Final Simplified Form: Now we can cancel out the common factor of 9x in the numerator and denominator: (-2 * (27x^2 - 2))/(9x * (x^2 - 25)) = (-2(27x^2 - 2))/(9x(x + 5)(x - 5)) = (-2 * 3 * (9x^2 - 1))/(9x(x + 5)(x - 5)) = (-6 * (9x^2 - 1))/(9x(x + 5)(x - 5))Finally, we cancel out the common factor of 9x in the numerator and denominator: (-6 * (9x^2 - 1))/(9x(x + 5)(x - 5)) = (-6/9) * ((9x^2 - 1)/(x(x + 5)(x - 5))) = (-2/3) * ((9x^2 - 1)/(x(x + 5)(x - 5)))The final simplified form of the expression is: (-2/3) * ((9x^2 - 1)/(x(x + 5)(x - 5)))

Subtract. $\newline$ The numerator should be expanded and simplified. The denominator should be either expanded or factored. $\newline$ $\frac{4}{9 x^{2}-45 x}-\frac{6 x}{x^{2}-25}=$

Full solution

More problems from Factor sums and differences of cubes

Related topics

Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline49x2−45x−6xx2−25= \frac{4}{9 x^{2}-45 x}-\frac{6 x}{x^{2}-25}= 9x2−45x4​−x2−256x​=

Subtract. $\newline$ The numerator should be expanded and simplified. The denominator should be either expanded or factored. $\newline$ $\frac{4}{9 x^{2}-45 x}-\frac{6 x}{x^{2}-25}=$