Add and Subtract the following dissimilar rational expressions.Show all your solutions.
1. 2/4x—2/8x+4/x²
2.7x—7/3x+6+x+2/3x+2
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Add and Subtract the following dissimilar rational expressions.Show all your solutions.
1. 2/4x—2/8x+4/x²
2.7x—7/3x+6+x+2/3x+2
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Verified answer
Answer:
1. x + 16/4x²
2. 63x³ + 171x² + 75x - 2/9x² + 24x + 12
Step-by-step explanation:
1.
[tex] \frac{2}{4x} - \frac{2}{8x} + \frac{4}{ {x}^{2} } [/tex]
[tex] \frac{2 \div 2}{4x \div 2} - \frac{2}{ 8x} + \frac{4}{ {x}^{2} } [/tex]
[tex] \frac{1}{2x} - \frac{2 \div 2}{8x \div 2} + \frac{4}{ {x}^{2} } [/tex]
[tex] \frac{1}{2x} - \frac{1}{4x} + \frac{4}{ {x}^{2} } [/tex]
[tex] \frac{1\times (2x)}{2x \times (2x)} - \frac{1 \times (x)}{4x \times (x)} + \frac{4 \times 4}{ {x}^{2} \times 4} [/tex]
[tex] \frac{2x}{4 {x}^{2} } - \frac{x}{4 {x}^{2} } + \frac{16}{4 {x}^{2} } [/tex]
[tex] \frac{2x - x + 16}{4 {x}^{2} } [/tex]
[tex] = \frac{x + 16}{4 {x}^{2} } [/tex]
2.
[tex]7x - \frac{7}{3x + 6} + \frac{x + 2}{3x + 2} [/tex]
[tex] \frac{7x \times (3x + 6)(3x + 2)}{(3x + 6)(3x + 2)} - \frac{7(3x + 2)}{(3x + 6)(3x + 2)} + \frac{(x + 2)(3x + 6)}{(3x + 2)(3x + 6)} [/tex]
[tex] \frac{7x \times (3x + 6)(3x + 2) - 7(3x + 2) + (x + 2)(3x + 6)}{(3x + 6)(3x + 2)} [/tex]
[tex] \frac{(21 {x}^{2} + 42x) \times (3x + 2) - 21x - 14 + 3(x + 2) \times (x + 2)}{9 {x}^{2} + 6x + 18x + 12 } [/tex]
[tex] \frac{63 {x}^{3} + 42 {x}^{2} + 126 {x}^{2} + 84x - 21x + 3(x - 2)^{2} }{9 {x}^{2} + 24x + 12 } [/tex]
[tex] \frac{63 {x}^{3} + 168 {x}^{2} + 63x - 14 + 3( {x}^{2} + 4x + 4) }{9 {x}^{2} + 24x + 12 } [/tex]
[tex] \frac{63 {x}^{3} + 168 {x}^{2} + 63x - 14 + 3 {x}^{2} + 12x + 12}{9 {x}^{2} + 24x + 12 } [/tex]
[tex] = \frac{63 {x}^{3} + 171 {x}^{2} + 75x - 2}{9 {x}^{2} + 24x + 12} [/tex]
1. 2/4x-2/8x+4/x^2
2/4x=1/2x
=1/2x - 2/8x + 4/x^2
2/8x=1/4x
=1/2x - 1/4 + 4/x^2
=2x/4x^2 - x/4x^2 + 16/2x^2
=2x-x+16/4x^2
=x+16/4x^2