Simplify: (3x)/(9x^(2)-16)-(1)/(3x+4)

Factor Denominator: Factor the denominator of the first fraction. The denominator is a difference of squares, which can be factored as follows: 9x^2 - 16 = (3x)^2 - 4^2 = (3x + 4)(3x - 4)Rewrite First Fraction: Rewrite the first fraction with the factored denominator. (3x)/(9x^2 - 16) becomes (3x)/((3x + 4)(3x - 4))Find Common Denominator: Find a common denominator for the two fractions. The common denominator will be the product of (3x + 4) and (3x - 4).Rewrite with Common Denominator: Rewrite both fractions with the common denominator. (3x)/((3x + 4)(3x - 4)) - (1)/(3x + 4) becomes (3x)/((3x + 4)(3x - 4)) - (3x - 4)/((3x + 4)(3x - 4))Combine Fractions: Combine the fractions. Now that they have a common denominator, we can combine the numerators: (3x - (3x - 4))/((3x + 4)(3x - 4))Simplify Numerator: Simplify the numerator. Distribute the negative sign in the second term of the numerator: 3x - 3x + 4 = 4Write Simplified Expression: Write the simplified expression. The simplified form of the expression is: 4/((3x + 4)(3x - 4))

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Simplify: $\newline$ $\left(\frac{3x}{9x^{2}-16}\right)-\left(\frac{1}{3x+4}\right)$

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Algebra 2

Simplify radical expressions involving fractions

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Q. Simplify:

\newline

\left(\frac{3x}{9x^{2}-16}\right)-\left(\frac{1}{3x+4}\right)

Factor Denominator: Factor the denominator of the first fraction. $\newline$ The denominator is a difference of squares, which can be factored as follows: $\newline$ $9x^2 - 16 = (3x)^2 - 4^2 = (3x + 4)(3x - 4)$
Rewrite First Fraction: Rewrite the first fraction with the factored denominator. $\newline$ $(3x)/(9x^2 - 16)$ becomes $(3x)/((3x + 4)(3x - 4))$
Find Common Denominator: Find a common denominator for the two fractions. $\newline$ The common denominator will be the product of $(3x + 4)$ and $(3x - 4)$ .
Rewrite with Common Denominator: Rewrite both fractions with the common denominator. $\newline$ $(3x)/((3x + 4)(3x - 4)) - (1)/(3x + 4)$ becomes $(3x)/((3x + 4)(3x - 4)) - (3x - 4)/((3x + 4)(3x - 4))$
Combine Fractions: Combine the fractions. $\newline$ Now that they have a common denominator, we can combine the numerators: $\newline$ $(3x - (3x - 4))/((3x + 4)(3x - 4))$
Simplify Numerator: Simplify the numerator. $\newline$ Distribute the negative sign in the second term of the numerator: $\newline$ $3x - 3x + 4 = 4$
Write Simplified Expression: Write the simplified expression. $\newline$ The simplified form of the expression is: $\newline$ $\frac{4}{(3x + 4)(3x - 4)}$