Express 2/(x+5) − 5/(3x−4) as a single fraction to its lowest form

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ScanSolve AI Tutor · Accepted Answer

Step 1: Find a common denominator for the two fractions. The denominators are (x+5) and (3x−4). The least common denominator (LCD) is the product of these two denominators: (x+5)(3x−4). Step 2: Rewrite each fraction with the common denominator. For the first fraction, multiply the numerator and denominator by (3x−4): (2)/(x+5) = (2(3x−4))/((x+5)(3x−4)) For the second fraction, multiply the numerator and denominator by (x+5): (5)/(3x−4) = (5(x+5))/((x+5)(3x−4)) Step 3: Subtract the rewritten fractions. (2(3x−4))/((x+5)(3x−4)) − (5(x+5))/((x+5)(3x−4)) = (2(3x−4) − 5(x+5))/((x+5)(3x−4)) Step 4: Expand the terms in the numerator. 2(3x−4) = 6x − 8; 5(x+5) = 5x + 25 Substitute these back into the numerator: (6x − 8) − (5x + 25) Step 5: Simplify the numerator by distributing the negative sign and combining like terms. 6x − 8 − 5x − 25 Combine the x terms: 6x − 5x = x; Combine the constant terms: −8 − 25 = −33 The simplified numerator is x − 33. Step 6: Write the expression as a single fraction in its lowest form. The numerator is x−33 and the denominator is (x+5)(3x−4). There are no common factors between the numerator and the denominator, so the fraction is in its lowest form. (x−33)/((x+5)(3x−4))

Express 2/(x+5) - 5/(3x-4) as a single fraction to its lowest form

Answer

Step-by-step solution

Find a common denominator for the two fractions.

Rewrite each fraction with the common denominator.

Subtract the rewritten fractions.

Expand the terms in the numerator.

Simplify the numerator by distributing the negative sign and combining like terms.

Write the expression as a single fraction in its lowest form.

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