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Adding 4m+3+3m+4\frac{4}{m+3} + \frac{3}{m+4}

To add the rational expressions 4m+3\frac{4}{m+3} and 3m+4\frac{3}{m+4}, determine the least common denominator (LCD). The denominators (m+3)(m+3) and (m+4)(m+4) have no common factors, so the LCD is (m+3)(m+4)(m+3)(m+4). Rewrite each rational expression with the LCD: 4(m+4)(m+3)(m+4)+3(m+3)(m+4)(m+3)\frac{4(m+4)}{(m+3)(m+4)} + \frac{3(m+3)}{(m+4)(m+3)}. Distribute the constants in the numerators to yield 4m+16(m+3)(m+4)+3m+9(m+3)(m+4)\frac{4m+16}{(m+3)(m+4)} + \frac{3m+9}{(m+3)(m+4)}. Add the numerators over the common denominator: 4m+16+3m+9(m+3)(m+4)\frac{4m+16+3m+9}{(m+3)(m+4)}. Combine like terms to simplify the numerator, resulting in the final expression: 7m+25(m+3)(m+4)\frac{7m+25}{(m+3)(m+4)}.

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Updated 2026-04-30

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References

Tags

OpenStax

Intermediate Algebra @ OpenStax

Ch.7 Rational Expressions and Functions - Intermediate Algebra @ OpenStax

Algebra

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