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Subtract.
The numerator should be expanded and simplified. The denominator should be either expanded or factored.

(8)/(x+3)-(2)/(x+8)=

Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline8x+32x+8= \frac{8}{x+3}-\frac{2}{x+8}=

Full solution

Q. Subtract.\newlineThe numerator should be expanded and simplified. The denominator should be either expanded or factored.\newline8x+32x+8= \frac{8}{x+3}-\frac{2}{x+8}=
  1. Identify common denominator: Identify the common denominator for the two fractions.\newlineTo subtract the fractions, we need a common denominator. The common denominator for (x+3)(x+3) and (x+8)(x+8) is the product of the two, which is (x+3)(x+8)(x+3)(x+8).
  2. Rewrite fractions with common denominator: Rewrite each fraction with the common denominator.\newlineWe need to express each fraction with the common denominator (x+3)(x+8)(x+3)(x+8). This means multiplying the numerator and denominator of each fraction by the necessary factor to achieve the common denominator.\newlineFor the first fraction, 8x+3\frac{8}{x+3}, we multiply the numerator and denominator by (x+8)(x+8).\newlineFor the second fraction, 2x+8\frac{2}{x+8}, we multiply the numerator and denominator by (x+3)(x+3).
  3. Perform multiplication for each fraction: Perform the multiplication for each fraction.\newlineNow we multiply the numerators and denominators as determined in Step 22.\newlineFirst fraction: (8×(x+8))/((x+3)(x+8))(8 \times (x+8)) / ((x+3)(x+8))\newlineSecond fraction: (2×(x+3))/((x+3)(x+8))(2 \times (x+3)) / ((x+3)(x+8))
  4. Expand numerators: Expand the numerators.\newlineWe need to expand the numerators of both fractions.\newlineFirst fraction's numerator: 8×(x+8)=8x+648 \times (x+8) = 8x + 64\newlineSecond fraction's numerator: 2×(x+3)=2x+62 \times (x+3) = 2x + 6
  5. Combine fractions by subtracting numerators: Combine the fractions by subtracting the numerators.\newlineNow that we have a common denominator, we can combine the fractions by subtracting the second fraction's numerator from the first fraction's numerator.\newline(8x+64)(2x+6)=8x+642x6(8x + 64) - (2x + 6) = 8x + 64 - 2x - 6
  6. Simplify the result: Simplify the result.\newlineSimplify the expression by combining like terms.\newline8x+642x6=(8x2x)+(646)=6x+588x + 64 - 2x - 6 = (8x - 2x) + (64 - 6) = 6x + 58
  7. Write the final answer: Write the final answer.\newlineThe final answer is the simplified numerator over the common denominator.\newline(6x+58)/((x+3)(x+8))(6x + 58) / ((x+3)(x+8))

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