The simplified value of 4x/(4x+3) – (4x²)/(4x+3)² is 12(x² + 1)/{16x² + 24x + 9}. The detailed solution for the same is added below:

Simplify 4x/(4x+3) – (4x²)/(4x+3)².

Solution:

Since the LCM of 4x + 3 and (4x + 3)² is (4x + 3)².

[Tex]\begin{aligned}\dfrac{4x}{4x+3}-\dfrac{4x^2}{(4x+3)^2}&\\=\dfrac{4x(4x+3)-4x^2}{(4x+3)^2}\\&\\=\dfrac{16x^2+12x-4x^2}{16x^2+24x+9}\\&\\=\dfrac{12x^2+12}{16x^2+24x+9}\end{aligned} [/Tex]

Similar Problems

Problem 1: Simplify: [Tex]\dfrac{p(p-8)+5(p-8)}{2p(p^2-8p-4p+32)}[/Tex].

Solution:

[Tex]\begin{aligned}\dfrac{4ab^2(-5ab^3)}{10a^2b^2}&=\dfrac{-20(a)^{1+1}(b)^{2+3}}{10a^2b^2}\\&= \dfrac{-2a^2b^5}{a^2b^2}\\&=-2a^{2-2}b^{5-2}\\&=-2(1)b^3\\&=-2b^3\end{aligned} [/Tex]

Problem 2: Simplify: [Tex]\dfrac{(p^{1/7})^{49}}{\left(\dfrac{14p^{1/2}}{(p^{26})^{-1/7}}\right)}. [/Tex]

Solution:

[Tex]\begin{aligned}\dfrac{(p^{1/7})^{49}}{\left(\dfrac{14p^{1/2}}{(p^{26})^{-1/7}}\right)}&=\dfrac{p^{49/7}}{\left(\dfrac{14p^{1/2}}{p^{-26/7}}\right)}\\&= \dfrac{p^7}{{14p^{1/2-(-26/7)}}} \\&= \dfrac{p^7}{{14p^{59/14}}}\\&= \dfrac{{p^{7-\frac{59}{14}}}}{14}\\&= \dfrac{p^{\frac{39}{14}}}{14}\end{aligned} [/Tex]

Problem 3: Simplify: 3x²(2xy – 3xy² + 4x²y³).

Solution:

P = 3x²(2xy − 3xy² + 4x²y³)

Since, a^m.aⁿ = a^m+n

P = 6×2+1y − 9×2+1y2 + 12×2+2y3

= 6x³y − 9x³y² + 12x⁴y³

Problem 4: Simplify: (25t^-4)/(5^-3 × 10t^-8).

Solution:

[25t^-4]/[5^-3 × 10 × t^-8]

= (5² × t⁻⁴)/(5⁻³ × 5 × 2 × t⁻⁸ )

= (5² × t−⁴⁾/(5⁻³⁺¹ × 2 × t⁻⁸) [Since, a^m × aⁿ = a^m+n]

= (5² × t⁻⁴)/(5⁻² × 2 × t⁻⁸)

= (5²⁻⁽⁻²⁾ × t^{−4−(−8)})/2 [Since, a^m/aⁿ = a^m−n]

= (5⁴ × t⁴)/2

= 625t⁴/2

Problem 5: Simplify: 1/2x^-99.

Solution:

Using the property a^-m = 1/ a^m, which is known as the Negative Exponent Law,

1/ 2x^-99

= 1/2(x⁹⁹) = (x⁹⁹)/2