How do you simplify #- 4/ (x - 5) + 7/ (2x + 3)#?

Question

Hazel Anglin · Accepted Answer

#(-x-47)/((2x+3)(x-5))# OR #(-x-47)/(2x^2-7x-15)#

Rearrange and write as:

#(7/(2x+3))-(4/(x-5))#

To simplify this, you need to make the denominators equal by finding their lowest common denominator (multiple). Whatever happens to the denominator, must happen to the numerator:

#7/((2x+3)(x-5))-4/((2x+3)(x-5))#

#(7(x-5))/((2x+3)(x-5))-(4(2x+3))/((2x+3)(x-5))#

Because the denominators now share the same LCM, you can merge them:

#(7(x-5)-4(2x+3))/((2x+3)(x-5))#

Multiply out all the brackets:

#(7x-35-8x-12)/(2x^2-10x+3x-15)#

Proceed to simplify terms:

#(-x-47)/(2x^2-7x-15)#

OR

Keep the denominator in the brackets:

#(-x-47)/((2x+3)(x-5))#

Avery Alexander · Answer

undefined To simplify the expression -4/(x - 5) + 7/(2x + 3), you need to find a common denominator for the two fractions. The common denominator is (x - 5)(2x + 3). Multiply the numerator and denominator of the first fraction by (2x + 3), and multiply the numerator and denominator of the second fraction by (x - 5). This gives you (-4)(2x + 3)/(x - 5)(2x + 3) + (7)(x - 5)/(x - 5)(2x + 3). Simplify the numerators and combine the fractions over the common denominator. The simplified expression is (-8x - 12 + 7x - 35)/(x - 5)(2x + 3). Combine like terms in the numerator to get (-x - 47)/(x - 5)(2x + 3).